diff --git a/changelog b/changelog
index 9fd4a40..e684837 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+20130727 tpd src/axiom-website/patches.html 20130727.01.tpd.patch
+20130727 tpd src/axiom-website/CATS/index.html add rich3c
+20130727 tpd src/axiom-website/CATS/rich3c.input added
+20130727 tpd src/axiom-website/CATS/rich3c.input.pdf added
+20130727 tpd src/input/Makefile add rich3c
+20130727 tpd src/input/rich3c.input added
20130726 tpd src/axiom-website/patches.html 20130726.01.tpd.patch
20130726 tpd src/axiom-website/CATS/index.html add rich3b
20130726 tpd src/axiom-website/CATS/rich3b.input added
diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html
index ad1f519..7303013 100644
--- a/src/axiom-website/CATS/index.html
+++ b/src/axiom-website/CATS/index.html
@@ -302,6 +302,9 @@ They have been rewritten using Axiom syntax.
(a+b x)^m (c+d)^n (e+f x)^p (part 2)
source
pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 3)
+ source
+ pdf
Rich
diff --git a/src/axiom-website/CATS/rich3c.input.pamphlet b/src/axiom-website/CATS/rich3c.input.pamphlet
new file mode 100644
index 0000000..88bdf31
--- /dev/null
+++ b/src/axiom-website/CATS/rich3c.input.pamphlet
@@ -0,0 +1,6734 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3c.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file
+\item 100 supplied "optimal results"
+\item 25 matching answers
+\item 12 answers that differ from the optimal results
+\item 58 cases that Axiom failed to integrate
+\item 5 that contain expressions Axiom does not recognize
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3c.output
+)spool rich3c.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=x^5/((a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 5
+--R x
+--R --------------------------------------------------------------------------
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=5/4*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+1/2*a*(b*c-5*a*d)*x^3/(b^2*d*_
+ (b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+1/2*x^4/(b*d*(c+d*x)^(3/2)*_
+ sqrt(a+b*x))+1/6*c*(7*b^2*c^2-6*a*b*c*d+15*a^2*d^2)*x^2*_
+ sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^2*(c+d*x)^(3/2))+1/6*_
+ c*(4*a*c*(7*b^2*c^2-6*a*b*c*d+15*a^2*d^2)+(35*b^3*c^3-_
+ 33*a*b^2*c^2*d-15*a^2*b*c*d^2+45*a^3*d^3)*x)*sqrt(a+b*x)/_
+ (b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x))-1/12*(3*b*c-a*d)*_
+ (35*b^3*c^3-33*a*b^2*c^2*d-15*a^2*b*c*d^2+45*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d
+--R +
+--R 5 5
+--R - 105b c d
+--R *
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6
+--R 45a c d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|d \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 2 6 2 3 5 4 2 4 5 3 3 4
+--R (6a b d - 18a b c d + 18a b c d - 6b c d )x
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3
+--R (- 15a b d + 24a b c d + 18a b c d - 48a b c d + 21b c d )x
+--R +
+--R 5 6 3 2 2 4 2 3 3 3 4 4 2 5 5 2
+--R (- 45a d + 66a b c d + 12a b c d - 237a b c d + 140b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 90a c d + 45a b c d + 84a b c d - 222a b c d - 50a b c d
+--R +
+--R 5 6
+--R 105b c
+--R *
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 45a c d + 30a b c d + 36a b c d - 190a b c d + 105a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 3 3 8 2 4 7 5 2 6 6 3 5 3 3 7
+--R (12a b d - 36a b c d + 36a b c d - 12b c d )x + 12a b c d
+--R +
+--R 2 4 2 6 5 3 5 6 4 4
+--R - 36a b c d + 36a b c d - 12b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 500
+--m0:=a0-r0
+--E 4
+
+--S 5 of 500
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=x^4/((a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R --------------------------------------------------------------------------
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=-(5*b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(5/2)*d^(7/2))+a*(b*c-3*a*d)*x^2/(b^2*d*(b*c-a*d)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x))+x^3/(b*d*(c+d*x)^(3/2)*sqrt(a+b*x))+1/3*c*_
+ (4*a*c*(b*c-3*a*d)+(b*c-a*d)*(5*b*c+3*a*d)*x)*sqrt(a+b*x)/_
+ (b^2*d^2*(b*c-a*d)^2*(c+d*x)^(3/2))+1/3*c*(15*b^3*c^3-_
+ 35*a*b^2*c^2*d+25*a^2*b*c*d^2-21*a^3*d^3)*sqrt(a+b*x)/_
+ (b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4
+--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c d)x - 9a c d
+--R +
+--R 3 2 3 2 2 3 2 3 4 4 5
+--R 12a b c d + 18a b c d - 36a b c d + 15b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|d \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 3
+--R (3a b d - 9a b c d + 9a b c d - 3b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2
+--R (9a d - 3a b c d - 9a b c d + 39a b c d - 20b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3
+--R (18a c d - 15a b c d + 33a b c d + 11a b c d - 15b c )x + 9a c d
+--R +
+--R 3 3 2 2 2 4 3 5
+--R - 9a b c d + 31a b c d - 15a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 3 2 7 2 3 6 4 2 5 5 3 4 3 2 6 2 3 2 5
+--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d
+--R +
+--R 4 3 4 5 4 3
+--R 9a b c d - 3b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 500
+--m0:=a0-r0
+--E 9
+
+--S 10 of 500
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=x^3/((a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R --------------------------------------------------------------------------
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))-_
+ 2*x^3/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+8/3*c*x^2*sqrt(a+b*x)/_
+ ((b*c-a*d)^2*(c+d*x)^(3/2))+4/3*c*(8*a*c+(b*c+3*a*d)*x)*_
+ sqrt(a+b*x)/(d*(b*c-a*d)^3*sqrt(c+d*x))-2/3*(3*b*c-a*d)*_
+ (b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (6a d - 18a b c d + 18a b c d - 6b c d)x + 6a c d - 18a b c d
+--R +
+--R 2 3 3 4
+--R 18a b c d - 6b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|d \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 4 2 2 2 3 3 2
+--R (- 6a d - 18a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3
+--R (- 12a c d - 18a b c d - 8a b c d + 6b c )x - 6a c d - 16a b c d
+--R +
+--R 2 4
+--R 6a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 3 6 2 2 5 3 2 4 4 3 3 3 5 2 2 2 4
+--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d
+--R +
+--R 3 3 3 4 4 2
+--R 9a b c d - 3b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 500
+--m0:=a0-r0
+--E 14
+
+--S 15 of 500
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=x^2/((a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R --------------------------------------------------------------------------
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-2*a^2/(b^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*(b^2*c^2+3*a^2*d^2)*_
+ sqrt(a+b*x)/(b^2*d*(b*c-a*d)^2*(c+d*x)^(3/2))+_
+ 2/3*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^3*_
+ sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 2
+--R (6a d + 12a b c d - 2b c )x + (24a c d + 8a b c )x + 16a c
+--R /
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d
+--R +
+--R 2 3 3 4
+--R 9a b c d - 3b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 2
+--R ((30a d + 60a b c d - 10b c )x + (120a c d + 40a b c )x + 80a c )
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 2 2 3 2 3 2 2 2 2
+--R (8a b c + 200a b)d x + ((8a c + 200a )d + (16a b c + 400a b c)d)x
+--R +
+--R 2 2 3 3 2 2 2 3 3 2
+--R ((16a c + 400a c)d + 8a b c + 200a b c )x + 8a c + 200a c
+--R /
+--R 3 5 2 2 4 3 2 3 4 3 2 3
+--R (15a b d - 45a b c d + 45a b c d - 15b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2
+--R (15a d - 15a b c d - 45a b c d + 75a b c d - 30b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3
+--R (30a c d - 75a b c d + 45a b c d + 15a b c d - 15b c )x + 15a c d
+--R +
+--R 3 3 2 2 2 4 3 5
+--R - 45a b c d + 45a b c d - 15a b c
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2
+--R 8a c + 200a
+--R (4) ----------------------------------------
+--R 3 3 2 2 2 2 3 3
+--R 15a d - 45a b c d + 45a b c d - 15b c
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=x/((a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R x
+--R --------------------------------------------------------------------------
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=2*a/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b*c+3*a*d)*_
+ sqrt(a+b*x)/(b*(b*c-a*d)^2*(c+d*x)^(3/2))+4/3*(b*c+3*a*d)*_
+ sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2
+--R (- 12a b d - 4b c d)x + (- 6a d - 20a b c d - 6b c )x - 4a c d
+--R +
+--R 2
+--R - 12a b c
+--R /
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d
+--R +
+--R 2 3 3 4
+--R 9a b c d - 3b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 3
+--R (- 36a b c d - 12b c d)x + (- 18a c d - 60a b c d - 18b c )x
+--R +
+--R 2 2 3
+--R - 12a c d - 36a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 2 3 2 2 2 2 3
+--R ((- 2a b c - 18a b)d + (- 6b c - 54a b c)d )x
+--R +
+--R 2 3 3 2 2 2
+--R (- 2a c - 18a )d + (- 10a b c - 90a b c)d
+--R +
+--R 2 3 2 2
+--R (- 12b c - 108a b c )d
+--R *
+--R 2
+--R x
+--R +
+--R 2 2 3 2 3 2 2 2 4 2 3
+--R ((- 4a c - 36a c)d + (- 14a b c - 126a b c )d - 6b c - 54a b c )x
+--R +
+--R 2 3 3 2 4 2 3
+--R (- 2a c - 18a c )d - 6a b c - 54a b c
+--R /
+--R 3 5 2 2 2 4 3 3 3 4 4 2 3
+--R (9a b c d - 27a b c d + 27a b c d - 9b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 2
+--R (9a c d - 9a b c d - 27a b c d + 45a b c d - 18b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4 3 3
+--R (18a c d - 45a b c d + 27a b c d + 9a b c d - 9b c )x + 9a c d
+--R +
+--R 3 4 2 2 2 5 3 6
+--R - 27a b c d + 27a b c d - 9a b c
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R (- 2a c - 18a )d - 6b c - 54a b c
+--R (4) ----------------------------------------
+--R 3 3 2 2 2 2 3 3 4
+--R 9a c d - 27a b c d + 27a b c d - 9b c
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=1/((a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R --------------------------------------------------------------------------
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=(-2)/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-_
+ 8/3*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(3/2))-_
+ 16/3*b*d*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 2
+--R 16b d x + (8a b d + 24b c d)x - 2a d + 12a b c d + 6b c
+--R /
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d
+--R +
+--R 2 3 3 4
+--R 9a b c d - 3b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 3 3 2 2 2 3
+--R 64a b c d x + (32a b c d + 96a b c d)x - 8a c d + 48a b c d
+--R +
+--R 2 4
+--R 24a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 2 3 4 2 2 2 2 3 3 3 3 2 2 3
+--R ((- a b c - 16a b)d + (6a b c + 96a b c)d + (3b c + 48a b c )d )x
+--R +
+--R 3 4 4 2 2 3 3 2 3 2 2 2 2
+--R (- a c - 16a )d + (4a b c + 64a b c)d + (15a b c + 240a b c )d
+--R +
+--R 3 4 3 3
+--R (6b c + 96a b c )d
+--R *
+--R 2
+--R x
+--R +
+--R 3 2 4 3 2 3 3 2 2
+--R (- 2a c - 32a c)d + (11a b c + 176a b c )d
+--R +
+--R 2 4 2 2 3 3 5 3 4
+--R (12a b c + 192a b c )d + 3b c + 48a b c
+--R *
+--R x
+--R +
+--R 3 3 4 2 2 2 4 3 3 2 5 2 2 4
+--R (- a c - 16a c )d + (6a b c + 96a b c )d + 3a b c + 48a b c
+--R /
+--R 4 2 5 3 2 3 4 2 3 4 3 4 5 2 3
+--R (12a b c d - 36a b c d + 36a b c d - 12a b c d )x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2
+--R (12a c d - 12a b c d - 36a b c d + 60a b c d - 24a b c d)x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3
+--R (24a c d - 60a b c d + 36a b c d + 12a b c d - 12a b c )x + 12a c d
+--R +
+--R 4 5 2 3 2 6 2 3 7
+--R - 36a b c d + 36a b c d - 12a b c
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 3 2 2 2 2 3 2 2
+--R (- a c - 16a )d + (6a b c + 96a b c)d + 3b c + 48a b c
+--R (4) ----------------------------------------------------------
+--R 4 2 3 3 3 2 2 2 4 3 5
+--R 12a c d - 36a b c d + 36a b c d - 12a b c
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=1/(x*(a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R ----------------------------------------------------------------------------
+--R 2 4 2 3 2 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))+_
+ 2*b/(a*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+_
+ 2/3*d*(3*b*c+a*d)*sqrt(a+b*x)/(a*c*(b*c-a*d)^2*(c+d*x)^(3/2))+_
+ 2/3*d*(3*b*c-a*d)*(b*c+3*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (- 6a d + 18a b c d - 18a b c d + 6b c d)x - 6a c d + 18a b c d
+--R +
+--R 2 3 3 4
+--R - 18a b c d + 6b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|c \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 2
+--R (6a b d - 16a b c d - 6b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (6a d - 8a b c d - 18a b c d - 12b c d)x + 8a c d - 18a b c d
+--R +
+--R 3 4
+--R - 6b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2
+--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x + 3a c d - 9a b c d
+--R +
+--R 2 2 5 3 6
+--R 9a b c d - 3a b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 500
+--m0:=a0-r0
+--E 34
+
+--S 35 of 500
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=1/(x^2*(a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------------
+--R 2 5 2 4 2 3 2 2 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=(3*b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(5/2)*c^(7/2))-b*(3*b*c-a*d)/(a^2*c*(b*c-a*d)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x))+(-1)/(a*c*x*(c+d*x)^(3/2)*sqrt(a+b*x))-_
+ 1/3*d*(9*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)/(a^2*_
+ c^2*(b*c-a*d)^2*(c+d*x)^(3/2))-1/3*d*(9*b^3*c^3-9*a*_
+ b^2*c^2*d+31*a^2*b*c*d^2-15*a^3*d^3)*sqrt(a+b*x)/(a^2*_
+ c^3*(b*c-a*d)^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2
+--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (15a c d - 36a b c d + 18a b c d + 12a b c d - 9b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|c \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 3
+--R (- 15a b d + 31a b c d - 9a b c d + 9b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2
+--R (- 15a d + 11a b c d + 33a b c d - 15a b c d + 18b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3
+--R (- 20a c d + 39a b c d - 9a b c d - 3a b c d + 9b c )x - 3a c d
+--R +
+--R 3 3 2 2 2 4 3 5
+--R 9a b c d - 9a b c d + 3a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2
+--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x
+--R +
+--R 5 4 3 4 5 2 3 2 6 2 3 7
+--R (3a c d - 9a b c d + 9a b c d - 3a b c )x
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 500
+--m0:=a0-r0
+--E 39
+
+--S 40 of 500
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=1/(x^3*(a+b*x)^(3/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------------
+--R 2 6 2 5 2 4 2 3 +-------+ +-------+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=-5/4*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))+1/4*b*(15*b^2*c^2-_
+ 7*a^2*d^2)/(a^3*c^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+_
+ (-1/2)/(a*c*x^2*(c+d*x)^(3/2)*sqrt(a+b*x))+1/4*(5*b*c+7*a*d)/_
+ (a^2*c^2*x*(c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(45*b^3*c^3-_
+ 15*a*b^2*c^2*d-33*a^2*b*c*d^2+35*a^3*d^3)*sqrt(a+b*x)/_
+ (a^3*c^3*(b*c-a*d)^2*(c+d*x)^(3/2))+1/12*d*(45*b^4*c^4-_
+ 30*a*b^3*c^3*d-36*a^2*b^2*c^2*d^2+190*a^3*b*c*d^3-105*a^4*d^4)*_
+ sqrt(a+b*x)/(a^3*c^4*(b*c-a*d)^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R - 105a d + 225a b c d - 90a b c d - 30a b c d - 45a b c d
+--R +
+--R 5 5
+--R 45b c d
+--R *
+--R 3
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 105a c d + 225a b c d - 90a b c d - 30a b c d - 45a b c d
+--R +
+--R 5 6
+--R 45b c
+--R *
+--R 2
+--R x
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|c \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 4
+--R (105a b d - 190a b c d + 36a b c d + 30a b c d - 45b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 105a d - 50a b c d - 222a b c d + 84a b c d + 45a b c d
+--R +
+--R 5 5
+--R - 90b c d
+--R *
+--R 3
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 6 2
+--R (140a c d - 237a b c d + 12a b c d + 66a b c d - 45b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R (21a c d - 48a b c d + 18a b c d + 24a b c d - 15a b c )x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6
+--R - 6a c d + 18a b c d - 18a b c d + 6a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 3
+--R (12a c d - 36a b c d + 36a b c d - 12a b c d)x
+--R +
+--R 6 5 3 5 6 2 4 2 7 3 3 8 2
+--R (12a c d - 36a b c d + 36a b c d - 12a b c )x
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 500
+--m0:=a0-r0
+--E 44
+
+--S 45 of 500
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=x^4*(c+d*x)^(5/2)/(a+b*x)^(5/2)
+--R
+--R
+--R 2 6 5 2 4 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ---------------------------------
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=-2/3*x^4*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+1/128*(b*c-a*d)*_
+ (3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*_
+ b*c*d^3+3003*a^4*d^4)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(15/2)*d^(5/2))-2/3*(8*b*c-13*a*d)*_
+ x^3*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))+1/192*_
+ (3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*_
+ b*c*d^3+3003*a^4*d^4)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^6*d^2*_
+ (b*c-a*d))-1/240*(15*b^3*c^3+125*a*b^2*c^2*d-2343*a^2*_
+ b*c*d^2+3003*a^3*d^3)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^5*d^2*_
+ (b*c-a*d))+1/120*(15*b^2*c^2-902*a*b*c*d+1287*a^2*d^2)*_
+ x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))+1/15*(93*_
+ b*c-143*a*d)*x^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))+_
+ 1/128*(3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-_
+ 2772*a^3*b*c*d^3+3003*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^7*d^2)
+--R
+--R
+--R (2)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 45045a b d + 86625a b c d - 47250a b c d + 5250a b c d
+--R +
+--R 5 4 6 5
+--R 375a b c d + 45b c
+--R *
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 45045a d + 86625a b c d - 47250a b c d + 5250a b c d
+--R +
+--R 2 4 4 5 5
+--R 375a b c d + 45a b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 6 4 6 5 4 6 3 5
+--R 384b d x + (- 624a b d + 1008b c d )x
+--R +
+--R 2 4 4 5 3 6 2 2 4
+--R (1144a b d - 1888a b c d + 744b c d )x
+--R +
+--R 3 3 4 2 4 3 5 2 2 6 3 3
+--R (- 2574a b d + 4378a b c d - 1834a b c d + 30b c d)x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2
+--R (9009a b d - 16038a b c d + 7404a b c d - 330a b c d - 45b c )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3
+--R 60060a b d - 97482a b c d + 38646a b c d - 750a b c d
+--R +
+--R 5 4
+--R - 90a b c
+--R *
+--R x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 45045a d - 71610a b c d + 27384a b c d - 390a b c d - 45a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 8 2 7 2 +-+ +-+ +-------+
+--R (1920b d x + 1920a b d )\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 500
+--m0:=a0-r0
+--E 49
+
+--S 50 of 500
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^(5/2)
+--R
+--R
+--R 2 5 4 2 3 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ---------------------------------
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=-2/3*x^3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))-5/64*(b*c-a*d)*_
+ (b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(13/2)*d^(3/2))-_
+ 2/3*(6*b*c-11*a*d)*x^2*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-_
+ 5/96*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/(b^5*d*(b*c-a*d))+1/24*(5*b^2*c^2-_
+ 156*a*b*c*d+231*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))+_
+ 1/12*(59*b*c-99*a*d)*x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))-_
+ 5/64*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^6*d)
+--R
+--R
+--R (2)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R (3465a b d - 6300a b c d + 3150a b c d - 300a b c d - 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3465a d - 6300a b c d + 3150a b c d - 300a b c d - 15a b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 3 5 4 3 5 2 4
+--R 48b d x + (- 88a b d + 136b c d )x
+--R +
+--R 2 3 3 4 2 5 2 3
+--R (198a b d - 316a b c d + 118b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 2
+--R (- 693a b d + 1161a b c d - 483a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 5 3
+--R (- 4620a b d + 7014a b c d - 2472a b c d + 30a b c )x - 3465a d
+--R +
+--R 4 2 3 2 2 2 3 3
+--R 5145a b c d - 1743a b c d + 15a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 7 6 +-+ +-+ +-------+
+--R (192b d x + 192a b d)\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 500
+--m0:=a0-r0
+--E 54
+
+--S 55 of 500
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^(5/2)
+--R
+--R
+--R 2 4 3 2 2 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ---------------------------------
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=-2/3*a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+_
+ 5/8*(b*c-a*d)*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*sqrt(d))+_
+ 4/3*a*(3*b*c-5*a*d)*(c+d*x)^(7/2)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))+_
+ 5/12*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (b^4*(b*c-a*d))+1/3*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(b^3*(b*c-a*d)^2)+5/8*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/b^5
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 4 3
+--R (- 315a b d + 525a b c d - 225a b c d + 15b c )x - 315a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 525a b c d - 225a b c d + 15a b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 2 4 3 2 4 3
+--R 8b d x + (- 18a b d + 26b c d)x
+--R +
+--R 2 2 2 3 4 2 2
+--R (63a b d - 96a b c d + 33b c )x
+--R +
+--R 3 2 2 2 3 2 4 2 3
+--R (420a b d - 574a b c d + 162a b c )x + 315a d - 420a b c d
+--R +
+--R 2 2 2
+--R 113a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 6 5 +-+ +-+ +-------+
+--R (24b x + 24a b )\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 500
+--m0:=a0-r0
+--E 59
+
+--S 60 of 500
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=x*(c+d*x)^(5/2)/(a+b*x)^(5/2)
+--R
+--R
+--R 2 3 2 2 +-------+
+--R (d x + 2c d x + c x)\|d x + c
+--R (1) --------------------------------
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=2/3*a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x)^(3/2))+5/4*(3*b*c-7*a*d)*_
+ (b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(d)/b^(9/2)-2/3*(3*b*c-7*a*d)*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*_
+ sqrt(a+b*x))+5/6*d*(3*b*c-7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (b^3*(b*c-a*d))+5/4*d*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^4
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 3 2 2 2 2
+--R ((105a b d - 150a b c d + 45b c )x + 105a d - 150a b c d + 45a b c )
+--R *
+--R +-+ +-------+
+--R +-+ +-------+ \|d \|b x + a
+--R \|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 2 3 2 2 3 2
+--R 6b d x + (- 21a b d + 27b c d)x
+--R +
+--R 2 2 2 3 2 3 2 2 2 2
+--R (- 140a b d + 158a b c d - 24b c )x - 105a d + 115a b c d - 16a b c
+--R *
+--R +-+ +-------+
+--R \|b \|d x + c
+--R /
+--R 5 4 +-+ +-------+
+--R (12b x + 12a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(c+d*x)^(5/2)/(a+b*x)^(5/2)
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=-2/3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+5*d^(3/2)*(b*c-a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-_
+ 10/3*d*(c+d*x)^(3/2)/(b^2*sqrt(a+b*x))+5*d^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ +-------+
+--R ((- 15a b d + 15b c d)x - 15a d + 15a b c d)\|d \|b x + a
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R (3b d x + (20a b d - 14b c d)x + 15a d - 10a b c d - 2b c )\|b
+--R *
+--R +-------+
+--R \|d x + c
+--R /
+--R 4 3 +-+ +-------+
+--R (3b x + 3a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(c+d*x)^(5/2)/(x*(a+b*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 3 2 2 +-------+
+--R (b x + 2a b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=2/3*(c+d*x)^(5/2)/(a*(a+b*x)^(3/2))-2*c^(5/2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(5/2)+2*d^(5/2)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)+_
+ 2/3*(3*b*c+2*a*d)*(c+d*x)^(3/2)/(a^2*b*sqrt(a+b*x))-_
+ 2*d*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*b^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 3 2 +-+ +-+ +-------+ \|d \|b x + a
+--R (6a b d x + 6a d )\|a \|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 2 2 2 +-+ +-+ +-------+ \|c \|b x + a
+--R (- 6b c x - 6a b c )\|b \|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 2 2 2 +-+ +-+
+--R ((- 8a b d + 2a b c d + 6b c )x - 6a d - 2a b c d + 8a b c )\|a \|b
+--R *
+--R +-------+
+--R \|d x + c
+--R /
+--R 2 3 3 2 +-+ +-+ +-------+
+--R (3a b x + 3a b )\|a \|b \|b x + a
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ---------------------------------
+--R 2 4 3 2 2 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=-5/3*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x)^(3/2))-(c+d*x)^(5/2)/_
+ (a*x*(a+b*x)^(3/2))+5*c^(3/2)*(b*c-a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(7/2)-5*c*(b*c-a*d)*_
+ sqrt(c+d*x)/(a^3*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 +-+ +-------+
+--R ((- 15a b c d + 15b c )x + (- 15a c d + 15a b c )x)\|c \|b x + a
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((2a d + 10a b c d - 15b c )x + (14a c d - 20a b c )x - 3a c )\|a
+--R *
+--R +-------+
+--R \|d x + c
+--R /
+--R 3 2 4 +-+ +-------+
+--R (3a b x + 3a x)\|a \|b x + a
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ---------------------------------
+--R 2 5 4 2 3 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=1/4*(7*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x)^(3/2))-1/2*(c+d*x)^(5/2)/_
+ (a*x^2*(a+b*x)^(3/2))-5/4*(7*b*c-3*a*d)*(b*c-a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(9/2)+_
+ 1/12*(35*b*c-29*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*(a+b*x)^(3/2))+_
+ 1/12*(105*b^2*c^2-115*a*b*c*d+16*a^2*d^2)*sqrt(c+d*x)/(a^4*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 3
+--R (- 45a b d + 150a b c d - 105b c )x
+--R +
+--R 3 2 2 2 2 2
+--R (- 45a d + 150a b c d - 105a b c )x
+--R *
+--R +-+ +-------+
+--R +-+ +-------+ \|c \|b x + a
+--R \|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 3 2 3
+--R (16a b d - 115a b c d + 105b c )x
+--R +
+--R 3 2 2 2 2 2 3 2 2 3 2
+--R (24a d - 158a b c d + 140a b c )x + (- 27a c d + 21a b c )x - 6a c
+--R *
+--R +-+ +-------+
+--R \|a \|d x + c
+--R /
+--R 4 3 5 2 +-+ +-------+
+--R (12a b x + 12a x )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 500
+--m0:=a0-r0
+--E 84
+
+--S 85 of 500
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ---------------------------------
+--R 2 6 5 2 4 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=1/12*(9*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x)^(3/2))-_
+ 1/3*(c+d*x)^(5/2)/(a*x^3*(a+b*x)^(3/2))+5/8*(b*c-a*d)*_
+ (21*b^2*c^2-14*a*b*c*d+a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*sqrt(c))-7/24*b*(15*b*c-7*a*d)*_
+ (b*c-a*d)*sqrt(c+d*x)/(a^4*(a+b*x)^(3/2))-1/8*(21*b*c-5*a*d)*_
+ (b*c-a*d)*sqrt(c+d*x)/(a^3*x*(a+b*x)^(3/2))-_
+ 1/24*b*(315*b^2*c^2-420*a*b*c*d+113*a^2*d^2)*sqrt(c+d*x)/(a^5*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 4
+--R (- 15a b d + 225a b c d - 525a b c d + 315b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 3
+--R (- 15a d + 225a b c d - 525a b c d + 315a b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 113a b d + 420a b c d - 315b c )x
+--R +
+--R 3 2 2 2 3 2 3
+--R (- 162a b d + 574a b c d - 420a b c )x
+--R +
+--R 4 2 3 2 2 2 2 4 3 2 4 2
+--R (- 33a d + 96a b c d - 63a b c )x + (- 26a c d + 18a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R /
+--R 5 4 6 3 +-+ +-+ +-------+
+--R (24a b x + 24a x )\|a \|c \|b x + a
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 500
+--m0:=a0-r0
+--E 89
+
+--S 90 of 500
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(c+d*x)^(5/2)/(x^5*(a+b*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ---------------------------------
+--R 2 7 6 2 5 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=1/24*(11*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^3*(a+b*x)^(3/2))-_
+ 1/4*(c+d*x)^(5/2)/(a*x^4*(a+b*x)^(3/2))-5/64*(b*c-a*d)*_
+ (231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(13/2)*_
+ c^(3/2))+1/64*b*(b*c-a*d)*(385*b^2*c^2-238*a*b*c*d+5*_
+ a^2*d^2)*sqrt(c+d*x)/(a^5*c*(a+b*x)^(3/2))-1/32*(33*b*c-_
+ 5*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*x^2*(a+b*x)^(3/2))+_
+ 1/64*(b*c-a*d)*(231*b^2*c^2-156*a*b*c*d+5*a^2*d^2)*_
+ sqrt(c+d*x)/(a^4*c*x*(a+b*x)^(3/2))+1/64*b*(1155*b^3*c^3-_
+ 1715*a*b^2*c^2*d+581*a^2*b*c*d^2-5*a^3*d^3)*sqrt(c+d*x)/_
+ (a^6*c*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (15a b d + 300a b c d - 3150a b c d + 6300a b c d - 3465b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d + 300a b c d - 3150a b c d + 6300a b c d - 3465a b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (- 15a b d + 1743a b c d - 5145a b c d + 3465b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 4
+--R (- 30a b d + 2472a b c d - 7014a b c d + 4620a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 3
+--R (- 15a d + 483a b c d - 1161a b c d + 693a b c )x
+--R +
+--R 5 2 4 2 3 2 3 2 5 2 4 3
+--R (- 118a c d + 316a b c d - 198a b c )x + (- 136a c d + 88a b c )x
+--R +
+--R 5 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R /
+--R 6 5 7 4 +-+ +-+ +-------+
+--R (192a b c x + 192a c x )\|a \|c \|b x + a
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 500
+--m0:=a0-r0
+--E 94
+
+--S 95 of 500
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=x^2/((a+b*x)^(5/2)*(c+d*x)^(1/2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------------------
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))-_
+ 2/3*a^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+_
+ 4/3*a*(3*b*c-2*a*d)*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 3 2 2 2 2
+--R ((6a b d - 12a b c d + 6b c )x + 6a d - 12a b c d + 6a b c )
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 3 2 +-+ +-+ +-------+
+--R ((- 8a b d + 12a b c)x - 6a d + 10a b c)\|b \|d \|d x + c
+--R /
+--R 2 3 2 4 5 2 3 2 2 2 3 4 2 +-+ +-+
+--R ((3a b d - 6a b c d + 3b c )x + 3a b d - 6a b c d + 3a b c )\|b \|d
+--R *
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 500
+--m0:=a0-r0
+--E 99
+
+--S 100 of 500
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=x^6/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 6
+--R x
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=1/6*a*(3*b*c-7*a*d)*x^4/(b^2*d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_
+ 1/2*x^5/(b*d*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5/4*(7*b^2*c^2+_
+ 10*a*b*c*d+7*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))+1/6*a*_
+ (3*b^2*c^2-62*a*b*c*d+35*a^2*d^2)*x^3/(b^3*d*(b*c-a*d)^2*_
+ (c+d*x)^(3/2)*sqrt(a+b*x))+1/6*c*(7*b^3*c^3-9*a*b^2*c^2*d+_
+ 69*a^2*b*c*d^2-35*a^3*d^3)*x^2*sqrt(a+b*x)/(b^3*d^2*(b*c-a*d)^3*_
+ (c+d*x)^(3/2))+1/6*c*(4*a*c*(7*b^3*c^3-9*a*b^2*c^2*d+_
+ 69*a^2*b*c*d^2-35*a^3*d^3)+(35*b^4*c^4-48*a*b^3*c^3*d-_
+ 18*a^2*b^2*c^2*d^2+200*a^3*b*c*d^3-105*a^4*d^4)*x)*_
+ sqrt(a+b*x)/(b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x))-_
+ 1/12*(3*b*c-a*d)*(35*b^4*c^4-48*a*b^3*c^3*d-18*a^2*b^2*c^2*d^2+_
+ 200*a^3*b*c*d^3-105*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3
+--R 105a b d - 270a b c d + 135a b c d + 60a b c d + 135a b c d
+--R +
+--R 6 5 2 7 6
+--R - 270a b c d + 105b c d
+--R *
+--R 2
+--R x
+--R +
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R 105a d - 165a b c d - 135a b c d + 195a b c d + 195a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R - 135a b c d - 165a b c d + 105b c
+--R *
+--R x
+--R +
+--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2
+--R 105a c d - 270a b c d + 135a b c d + 60a b c d + 135a b c d
+--R +
+--R 2 5 6 6 7
+--R - 270a b c d + 105a b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|d \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 5
+--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x
+--R +
+--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3
+--R - 21a b d + 63a b c d - 42a b c d - 42a b c d + 63a b c d
+--R +
+--R 7 5 2
+--R - 21b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3
+--R - 140a b d + 276a b c d + 12a b c d - 168a b c d + 12a b c d
+--R +
+--R 6 5 2 7 6
+--R 276a b c d - 140b c d
+--R *
+--R 3
+--R x
+--R +
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R - 105a d - 45a b c d + 549a b c d - 207a b c d - 207a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R 549a b c d - 45a b c d - 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 6 6 2 5 5 2 3 4 4 3 4 3
+--R - 210a c d + 330a b c d + 186a b c d - 228a b c d
+--R +
+--R 3 4 5 2 2 5 6 6 7
+--R 186a b c d + 330a b c d - 210a b c
+--R *
+--R x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6
+--R - 105a c d + 235a b c d - 66a b c d - 66a b c d + 235a b c d
+--R +
+--R 2 5 7
+--R - 105a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 4 5 9 3 6 8 2 7 2 7 8 3 6 9 4 5 2
+--R (12a b d - 48a b c d + 72a b c d - 48a b c d + 12b c d )x
+--R +
+--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5
+--R 12a b d - 36a b c d + 24a b c d + 24a b c d - 36a b c d
+--R +
+--R 9 5 4
+--R 12b c d
+--R *
+--R x
+--R +
+--R 5 4 8 4 5 2 7 3 6 3 6 2 7 4 5 8 5 4
+--R 12a b c d - 48a b c d + 72a b c d - 48a b c d + 12a b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 500
+--m0:=a0-r0
+--E 104
+
+--S 105 of 500
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=x^5/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 5
+--R x
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=1/3*a*(3*b*c-5*a*d)*x^3/(b^2*d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_
+ x^4/(b*d*(a+b*x)^(3/2)*(c+d*x)^(3/2))-5*(b*c+a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+_
+ a*(b^2*c^2-10*a*b*c*d+5*a^2*d^2)*x^2/(b^3*d*(b*c-a*d)^2*_
+ (c+d*x)^(3/2)*sqrt(a+b*x))+1/3*c*(4*a*c*(b^2*c^2-10*a*b*c*d+_
+ 5*a^2*d^2)+5*(b*c-a*d)^2*(b*c+a*d)*x)*sqrt(a+b*x)/(b^3*d^2*_
+ (b*c-a*d)^3*(c+d*x)^(3/2))+1/3*c*(15*b^4*c^4-44*a*b^3*c^3*d+_
+ 62*a^2*b^2*c^2*d^2-100*a^3*b*c*d^3+35*a^4*d^4)*sqrt(a+b*x)/_
+ (b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R - 15a b d + 45a b c d - 30a b c d - 30a b c d + 45a b c d
+--R +
+--R 6 5
+--R - 15b c d
+--R *
+--R 2
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 15a d + 30a b c d + 15a b c d - 60a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R 30a b c d - 15b c
+--R *
+--R x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5
+--R - 15a c d + 45a b c d - 30a b c d - 30a b c d + 45a b c d
+--R +
+--R 5 6
+--R - 15a b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|d \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R 20a b d - 48a b c d + 12a b c d + 12a b c d - 48a b c d
+--R +
+--R 6 5
+--R 20b c d
+--R *
+--R 3
+--R x
+--R +
+--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2
+--R (15a d - 87a b c d + 48a b c d - 87a b c d + 15b c )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5
+--R 30a c d - 60a b c d - 18a b c d - 18a b c d - 60a b c d
+--R +
+--R 5 6
+--R 30a b c
+--R *
+--R x
+--R +
+--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6
+--R 15a c d - 40a b c d + 18a b c d - 40a b c d + 15a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 2
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x
+--R +
+--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3
+--R (3a b d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c d )x
+--R +
+--R 5 3 7 4 4 2 6 3 5 3 5 2 6 4 4 7 5 3
+--R 3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 500
+--m0:=a0-r0
+--E 109
+
+--S 110 of 500
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=x^4/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=-2/3*x^4/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_
+ 4/3*(4*b*c-a*d)*x^3/(b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_
+ 4/3*c*(5*b*c-a*d)*x^2*sqrt(a+b*x)/(b*(b*c-a*d)^3*(c+d*x)^(3/2))+_
+ 4/3*c*(4*a*c*(5*b*c-a*d)+(b^2*c^2+10*a*b*c*d-3*a^2*d^2)*x)*_
+ sqrt(a+b*x)/(b*d*(b*c-a*d)^4*sqrt(c+d*x))-2/3*(3*b*c-a*d)*_
+ (b^2*c^2+10*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_
+ (b^2*d^2*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (6a d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R 6a c d - 24a b c d + 36a b c d - 24a b c d + 6a b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|d \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 3
+--R (- 8a b d + 24a b c d + 24a b c d - 8b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2
+--R (- 6a d + 6a b c d + 48a b c d + 48a b c d + 6a b c d - 6b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R (- 12a c d + 36a b c d + 48a b c d + 36a b c d - 12a b c )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5
+--R - 6a c d + 22a b c d + 22a b c d - 6a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 2
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x
+--R +
+--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2
+--R (3a b d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c d )x
+--R +
+--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2
+--R 3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 500
+--m0:=a0-r0
+--E 114
+
+--S 115 of 500
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=x^3/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=-2/3*x^3/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-4*a^2*c/_
+ (b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-4/3*c*_
+ (b^2*c^2+3*a^2*d^2)*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^3*(c+d*x)^(3/2))+_
+ 4/3*c*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^4*_
+ sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 3
+--R (2a d - 18a b c d - 18a b c d + 2b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (- 12a c d - 72a b c d - 12a b c )x + (- 48a c d - 48a b c )x - 32a c
+--R /
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 3
+--R (2a d - 18a b c d - 18a b c d + 2b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 12a c d - 72a b c d - 12a b c )x + (- 48a c d - 48a b c )x
+--R +
+--R 3 3
+--R - 32a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 2 2 2 2 2 4
+--R (16a b c + 16a b c)d x
+--R +
+--R 2 2 3 2 2 3 2 2 2 3
+--R ((32a b c + 32a b c)d + (32a b c + 32a b c )d)x
+--R +
+--R 3 2 4 2 2 3 3 2 2 4 2 2 3 2
+--R ((16a c + 16a c)d + (64a b c + 64a b c )d + 16a b c + 16a b c )x
+--R +
+--R 3 3 4 2 2 4 3 3 3 4 4 3
+--R ((32a c + 32a c )d + 32a b c + 32a b c )x + 16a c + 16a c
+--R /
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3
+--R (6a b d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6b c d)x
+--R +
+--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2
+--R (3a d - 27a b c d + 48a b c d - 27a b c d + 3b c )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6
+--R (6a c d - 18a b c d + 12a b c d + 12a b c d - 18a b c d + 6a b c )x
+--R +
+--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6
+--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R 16a c + 16a c
+--R (4) ---------------------------------------------------
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3a d - 12a b c d + 18a b c d - 12a b c d + 3b c
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=x^2/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=-2/3*a^2/(b^2*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*a*c/_
+ (b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b^2*c^2+_
+ 6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b^2*(b*c-a*d)^3*(c+d*x)^(3/2))+_
+ 4/3*(b^2*c^2+6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b*(b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 3 2 3
+--R (4a b d + 24a b c d + 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2
+--R (6a d + 42a b c d + 42a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2 3
+--R (24a c d + 48a b c d + 24a b c )x + 16a c d + 16a b c
+--R /
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 3 2 3
+--R (12a b d + 72a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2
+--R (18a d + 126a b c d + 126a b c d + 18b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2 3
+--R (72a c d + 144a b c d + 72a b c )x + 48a c d + 48a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 2 2 2 3 3 2 3 2 4
+--R ((8a b c + 72a b )d + (8b c + 72a b c)d )x
+--R +
+--R 2 3 3 2 2 2 2 2
+--R (16a b c + 144a b)d + (32a b c + 288a b c)d
+--R +
+--R 3 3 3 2
+--R (16b c + 144a b c )d
+--R *
+--R 3
+--R x
+--R +
+--R 3 4 3 2 2 3 2 2 3 2 2 2
+--R (8a c + 72a )d + (40a b c + 360a b c)d + (40a b c + 360a b c )d
+--R +
+--R 3 4 3 3
+--R 8b c + 72a b c
+--R *
+--R 2
+--R x
+--R +
+--R 3 2 4 2 2 3 3 2 2 4 2 2 3
+--R ((16a c + 144a c)d + (32a b c + 288a b c )d + 16a b c + 144a b c )x
+--R +
+--R 3 3 4 2 2 4 3 3
+--R (8a c + 72a c )d + 8a b c + 72a b c
+--R /
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4
+--R (9a b d - 36a b c d + 54a b c d - 36a b c d + 9b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R 18a b d - 54a b c d + 36a b c d + 36a b c d - 54a b c d
+--R +
+--R 6 5
+--R 18b c d
+--R *
+--R 3
+--R x
+--R +
+--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2
+--R (9a d - 81a b c d + 144a b c d - 81a b c d + 9b c )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6
+--R (18a c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d + 18a b c )x
+--R +
+--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6
+--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R (8a c + 72a )d + 8b c + 72a b c
+--R (4) ---------------------------------------------------
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R 9a d - 36a b c d + 54a b c d - 36a b c d + 9b c
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=x/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R x
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=-2/3*c/(d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2/3*(b*c+a*d)/_
+ (d*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x))-8/3*(b*c+a*d)/_
+ ((b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x))-16/3*d*(b*c+a*d)*_
+ sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 3 2 3 2 3 2 2 3 2 2
+--R (- 16a b d - 16b c d )x + (- 24a b d - 48a b c d - 24b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3
+--R (- 6a d - 42a b c d - 42a b c d - 6b c )x - 4a c d - 24a b c d - 4a b c
+--R /
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 3 2 2 3
+--R (- 48a b c d - 48a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3 2
+--R (- 72a b c d - 144a b c d - 72a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 2
+--R (- 18a c d - 126a b c d - 126a b c d - 18a b c )x - 12a c d
+--R +
+--R 3 3 2 2 4
+--R - 72a b c d - 12a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 2 2 3 2 4 3 2 2 3 3
+--R (- 2a b c - 18a b )d + (- 12a b c - 108a b c)d
+--R +
+--R 4 3 4 2 2
+--R (- 2b c - 18a b c )d
+--R *
+--R 4
+--R x
+--R +
+--R 3 4 4 2 2 2 3 2 3
+--R (- 4a b c - 36a b)d + (- 28a b c - 252a b c)d
+--R +
+--R 3 3 2 3 2 2 4 4 4 3
+--R (- 28a b c - 252a b c )d + (- 4b c - 36a b c )d
+--R *
+--R 3
+--R x
+--R +
+--R 4 5 4 3 2 4 3
+--R (- 2a c - 18a )d + (- 20a b c - 180a b c)d
+--R +
+--R 2 2 3 3 2 2 2 3 4 2 3 3 4 5
+--R (- 52a b c - 468a b c )d + (- 20a b c - 180a b c )d - 2b c
+--R +
+--R 4 4
+--R - 18a b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 2 5 3 3 3 4 2 2
+--R (- 4a c - 36a c)d + (- 28a b c - 252a b c )d
+--R +
+--R 2 2 4 3 2 3 3 5 2 3 4
+--R (- 28a b c - 252a b c )d - 4a b c - 36a b c
+--R *
+--R x
+--R +
+--R 4 3 5 2 2 3 4 4 3 2 2 5 3 2 4
+--R (- 2a c - 18a c )d + (- 12a b c - 108a b c )d - 2a b c - 18a b c
+--R /
+--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 4
+--R (9a b c d - 36a b c d + 54a b c d - 36a b c d + 9a b c d )x
+--R +
+--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2
+--R 18a b c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d
+--R +
+--R 6 6
+--R 18a b c d
+--R *
+--R 3
+--R x
+--R +
+--R 7 6 5 2 3 4 4 3 4 3 3 4 5 2 6 7 2
+--R (9a c d - 81a b c d + 144a b c d - 81a b c d + 9a b c )x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
+--R (18a c d - 54a b c d + 36a b c d + 36a b c d - 54a b c d + 18a b c )x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7
+--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 3 2 2 2 2 3 2 2
+--R (- 2a c - 18a )d + (- 12a b c - 108a b c)d - 2b c - 18a b c
+--R (4) ---------------------------------------------------------------
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R 9a c d - 36a b c d + 54a b c d - 36a b c d + 9a b c
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=1/((a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*d/((b*c-a*d)^2*_
+ (c+d*x)^(3/2)*sqrt(a+b*x))+16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*_
+ (c+d*x)^(3/2))+32/3*b*d^2*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2
+--R 32b d x + (48a b d + 48b c d )x + (12a b d + 72a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R - 2a d + 18a b c d + 18a b c d - 2b c
+--R /
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 3 3 3 2 2 3 2 3 3 2 2
+--R 160a b c d x + (240a b c d + 240a b c d )x
+--R +
+--R 4 2 3 3 2 3 2 2 3 4 5 2 3 4 3 2
+--R (60a b c d + 360a b c d + 60a b c d)x - 10a c d + 90a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 90a b c d - 10a b c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R +
+--R 3 2 4 2 5 2 3 2 3 3 4
+--R (- a b c - 25a b )d + (9a b c + 225a b c)d
+--R +
+--R 4 3 2 4 2 3 5 4 5 3 2
+--R (9a b c + 225a b c )d + (- b c - 25a b c )d
+--R *
+--R 4
+--R x
+--R +
+--R 4 5 5 3 2 2 4 2 4
+--R (- 2a b c - 50a b)d + (16a b c + 400a b c)d
+--R +
+--R 2 3 3 3 3 2 3 4 4 2 4 3 2
+--R (36a b c + 900a b c )d + (16a b c + 400a b c )d
+--R +
+--R 5 5 5 4
+--R (- 2b c - 50a b c )d
+--R *
+--R 3
+--R x
+--R +
+--R 5 6 5 4 2 5 4 3 2 3 4 2 2 3
+--R (- a c - 25a )d + (5a b c + 125a b c)d + (44a b c + 1100a b c )d
+--R +
+--R 2 3 4 3 3 3 2 4 5 2 4 4 5 6 5 5
+--R (44a b c + 1100a b c )d + (5a b c + 125a b c )d - b c - 25a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 6 4 4 3 5 2 3
+--R (- 2a c - 50a c)d + (16a b c + 400a b c )d
+--R +
+--R 3 2 4 4 2 3 2 2 3 5 3 3 4 4 6 2 4 5
+--R (36a b c + 900a b c )d + (16a b c + 400a b c )d - 2a b c - 50a b c
+--R *
+--R x
+--R +
+--R 5 3 6 2 3 4 4 5 3 2 3 2 5 4 2 4
+--R (- a c - 25a c )d + (9a b c + 225a b c )d + (9a b c + 225a b c )d
+--R +
+--R 2 3 6 3 3 5
+--R - a b c - 25a b c
+--R /
+--R 6 2 2 6 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2 4
+--R (15a b c d - 60a b c d + 90a b c d - 60a b c d + 15a b c d )x
+--R +
+--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2
+--R 30a b c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d
+--R +
+--R 2 6 7
+--R 30a b c d
+--R *
+--R 3
+--R x
+--R +
+--R 8 2 6 6 2 4 4 5 3 5 3 4 4 6 2 2 6 8 2
+--R (15a c d - 135a b c d + 240a b c d - 135a b c d + 15a b c )x
+--R +
+--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8
+--R (30a c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d + 30a b c )x
+--R +
+--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8
+--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 4 3 2 2 3 2 2 3 2 2 2 3 4
+--R (- a c - 25a )d + (9a b c + 225a b c)d + (9a b c + 225a b c )d - b c
+--R +
+--R 3 3
+--R - 25a b c
+--R /
+--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6
+--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=1/(x*(a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 5 2 2 4 2 2 2 2 3
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=2/3*b/(a*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-2*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+_
+ 2*b*(b*c-3*a*d)/(a^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_
+ 2/3*d*(3*b^2*c^2-10*a*b*c*d-a^2*d^2)*sqrt(a+b*x)/(a^2*c*(b*c-a*d)^3*_
+ (c+d*x)^(3/2))+2/3*d*(b*c+a*d)*(3*b^2*c^2-14*a*b*c*d+3*a^2*d^2)*_
+ sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (- 6a b d + 24a b c d - 36a b c d + 24a b c d - 6b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 6a d + 18a b c d - 12a b c d - 12a b c d + 18a b c d - 6b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5
+--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|c \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 2 5 2 3 4 4 2 3 5 3 2 3
+--R (6a b d - 22a b c d - 22a b c d + 6b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2
+--R (12a b d - 36a b c d - 48a b c d - 36a b c d + 12b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (6a d - 6a b c d - 48a b c d - 48a b c d - 6a b c d + 6b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5
+--R 8a c d - 24a b c d - 24a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 2 5 6 2
+--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
+--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7
+--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 500
+--m0:=a0-r0
+--E 139
+
+--S 140 of 500
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=1/(x^2*(a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 6 2 2 5 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=-1/3*b*(5*b*c-3*a*d)/(a^2*c*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1)/_
+ (a*c*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5*(b*c+a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_
+ b*(5*b^2*c^2-10*a*b*c*d+a^2*d^2)/(a^3*c*(b*c-a*d)^2*(c+d*x)^(3/2)*_
+ sqrt(a+b*x))-1/3*d*(15*b^3*c^3-35*a*b^2*c^2*d+9*a^2*b*c*d^2-_
+ 5*a^3*d^3)*sqrt(a+b*x)/(a^3*c^2*(b*c-a*d)^3*(c+d*x)^(3/2))-_
+ 1/3*d*(15*b^4*c^4-40*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+_
+ 15*a^4*d^4)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R 15a b d - 45a b c d + 30a b c d + 30a b c d - 45a b c d
+--R +
+--R 6 5
+--R 15b c d
+--R *
+--R 3
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 15a d - 30a b c d - 15a b c d + 60a b c d - 15a b c d
+--R +
+--R 5 5 6 6
+--R - 30a b c d + 15b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5
+--R 15a c d - 45a b c d + 30a b c d + 30a b c d - 45a b c d
+--R +
+--R 5 6
+--R 15a b c
+--R *
+--R x
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|c \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4
+--R (- 15a b d + 40a b c d - 18a b c d + 40a b c d - 15b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R - 30a b d + 60a b c d + 18a b c d + 18a b c d + 60a b c d
+--R +
+--R 6 5
+--R - 30b c d
+--R *
+--R 3
+--R x
+--R +
+--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2
+--R (- 15a d + 87a b c d - 48a b c d + 87a b c d - 15b c )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5
+--R - 20a c d + 48a b c d - 12a b c d - 12a b c d + 48a b c d
+--R +
+--R 5 6
+--R - 20a b c
+--R *
+--R x
+--R +
+--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6
+--R - 3a c d + 12a b c d - 18a b c d + 12a b c d - 3a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 3 5 7 3
+--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x
+--R +
+--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 2
+--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x
+--R +
+--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8
+--R (3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c )x
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 500
+--m0:=a0-r0
+--E 144
+
+--S 145 of 500
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=1/(x^3*(a+b*x)^(5/2)*(c+d*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 7 2 2 6 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=1/12*b*(35*b^2*c^2-6*a*b*c*d-21*a^2*d^2)/(a^3*c^2*(b*c-a*d)*_
+ (a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1/2)/(a*c*x^2*(a+b*x)^(3/2)*_
+ (c+d*x)^(3/2))+7/4*(b*c+a*d)/(a^2*c^2*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))-_
+ 5/4*(7*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))+1/4*b*(35*b^3*c^3-_
+ 55*a*b^2*c^2*d-3*a^2*b*c*d^2+7*a^3*d^3)/(a^4*c^2*(b*c-a*d)^2*_
+ (c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(105*b^4*c^4-200*a*b^3*c^3*d+_
+ 18*a^2*b^2*c^2*d^2+48*a^3*b*c*d^3-35*a^4*d^4)*sqrt(a+b*x)/_
+ (a^4*c^3*(b*c-a*d)^3*(c+d*x)^(3/2))+1/12*d*(b*c+a*d)*(105*b^4*c^4-_
+ 340*a*b^3*c^3*d+406*a^2*b^2*c^2*d^2-340*a^3*b*c*d^3+105*a^4*d^4)*_
+ sqrt(a+b*x)/(a^4*c^4*(b*c-a*d)^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 6 7 5 2 6 4 3 2 5 3 4 3 4
+--R - 105a b d + 270a b c d - 135a b c d - 60a b c d
+--R +
+--R 2 5 4 3 6 5 2 7 6
+--R - 135a b c d + 270a b c d - 105b c d
+--R *
+--R 4
+--R x
+--R +
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R - 105a d + 165a b c d + 135a b c d - 195a b c d - 195a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R 135a b c d + 165a b c d - 105b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 6 6 2 5 5 2 3 4 4 3 4 3
+--R - 105a c d + 270a b c d - 135a b c d - 60a b c d
+--R +
+--R 3 4 5 2 2 5 6 6 7
+--R - 135a b c d + 270a b c d - 105a b c
+--R *
+--R 2
+--R x
+--R *
+--R +-+ +-------+
+--R +-------+ +-------+ \|c \|b x + a
+--R \|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3
+--R 105a b d - 235a b c d + 66a b c d + 66a b c d - 235a b c d
+--R +
+--R 7 5 2
+--R 105b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3
+--R 210a b d - 330a b c d - 186a b c d + 228a b c d - 186a b c d
+--R +
+--R 6 5 2 7 6
+--R - 330a b c d + 210b c d
+--R *
+--R 4
+--R x
+--R +
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R 105a d + 45a b c d - 549a b c d + 207a b c d + 207a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R - 549a b c d + 45a b c d + 105b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2
+--R 140a c d - 276a b c d - 12a b c d + 168a b c d - 12a b c d
+--R +
+--R 2 5 6 6 7
+--R - 276a b c d + 140a b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6
+--R 21a c d - 63a b c d + 42a b c d + 42a b c d - 63a b c d
+--R +
+--R 2 5 7
+--R 21a b c
+--R *
+--R x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7
+--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 8 4 5 7 2 5 4 6 3 6 3 5 4 7 2 4 5 8 4
+--R (12a b c d - 48a b c d + 72a b c d - 48a b c d + 12a b c d)x
+--R +
+--R 9 4 5 8 5 4 7 2 6 3 6 3 7 2 5 4 8
+--R 12a c d - 36a b c d + 24a b c d + 24a b c d - 36a b c d
+--R +
+--R 4 5 9
+--R 12a b c
+--R *
+--R 3
+--R x
+--R +
+--R 9 5 4 8 6 3 7 2 7 2 6 3 8 5 4 9 2
+--R (12a c d - 48a b c d + 72a b c d - 48a b c d + 12a b c )x
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 500
+--m0:=a0-r0
+--E 149
+
+--S 150 of 500
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=x^2*sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R 2 +-------+
+--R x \|b x + a
+--R (1) ------------
+--R +---------+
+--R \|- b x - a
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=1/3*x^3*sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R 3 +-------+
+--R x \|b x + a
+--R (2) -------------
+--R +---------+
+--R 3\|- b x - a
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 +---------+ +-------+
+--R x \|- b x - a \|b x + a
+--R (3) - ------------------------
+--R 3b x + 3a
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=x*sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R +-------+
+--R x\|b x + a
+--R (1) ------------
+--R +---------+
+--R \|- b x - a
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=1/2*x^2*sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R 2 +-------+
+--R x \|b x + a
+--R (2) -------------
+--R +---------+
+--R 2\|- b x - a
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +---------+ +-------+
+--R x \|- b x - a \|b x + a
+--R (3) - ------------------------
+--R 2b x + 2a
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ------------
+--R +---------+
+--R \|- b x - a
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=x*sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R +-------+
+--R x\|b x + a
+--R (2) ------------
+--R +---------+
+--R \|- b x - a
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+ +-------+
+--R x\|- b x - a \|b x + a
+--R (3) - -----------------------
+--R b x + a
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=sqrt(a+b*x)/(x*sqrt(-a-b*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) -------------
+--R +---------+
+--R x\|- b x - a
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=log(x)*sqrt(a+b*x)/sqrt(-a-b*x)
+--R
+--R
+--R +-------+
+--R log(x)\|b x + a
+--R (2) ----------------
+--R +---------+
+--R \|- b x - a
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 500
+--m0:=a0-r0
+--E 169
+
+--S 170 of 500
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=sqrt(a+b*x)/(x^2*sqrt(-a-b*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) --------------
+--R 2 +---------+
+--R x \|- b x - a
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=-sqrt(a+b*x)/(x*sqrt(-a-b*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (2) - -------------
+--R +---------+
+--R x\|- b x - a
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 500
+--m0:=a0-r0
+--E 174
+
+--S 175 of 500
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=sqrt(a+b*x)/(x^3*sqrt(-a-b*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) --------------
+--R 3 +---------+
+--R x \|- b x - a
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=-1/2*sqrt(a+b*x)/(x^2*sqrt(-a-b*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (2) - ---------------
+--R 2 +---------+
+--R 2x \|- b x - a
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500 "Error detected within library code: Shouldn't happen"
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +---------+ +-------+
+--R (- x + 1)\|- b x - a \|b x + a
+--R (3) --------------------------------
+--R 3 2
+--R 2b x + 2a x
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (4) -------------
+--R +---------+
+--R 2\|- b x - a
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=sqrt(a+b*x)/(x^m*sqrt(-a-b*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) --------------
+--R m +---------+
+--R x \|- b x - a
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=x^(1-m)*sqrt(a+b*x)/((1-m)*sqrt(-a-b*x))
+--R
+--R
+--R - m + 1 +-------+
+--R x \|b x + a
+--R (2) - -------------------
+--R +---------+
+--R (m - 1)\|- b x - a
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 500
+--m0:=a0-r0
+--E 184
+
+--S 185 of 500
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=x^2*(a+b*x)^n/(-a-b*x)^n
+--R
+--R
+--R 2 n
+--R x (b x + a)
+--R (1) ------------
+--R n
+--R (- b x - a)
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=1/3*x^3*(a+b*x)^n/(-a-b*x)^n
+--R
+--R
+--R 3 n
+--R x (b x + a)
+--R (2) -------------
+--R n
+--R 3(- b x - a)
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R x cos(n %pi)
+--R (3) ---------------------------
+--R 2 2
+--R 3sin(n %pi) + 3cos(n %pi)
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R 3 2 3 2 n 3 n
+--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a)
+--R (4) ----------------------------------------------------------------------
+--R 2 2 n
+--R (3sin(n %pi) + 3cos(n %pi) )(- b x - a)
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 2 2 n
+--R (- 3x sin(n %pi) - 3x cos(n %pi) )(- b x - a)
+--R +
+--R 3 2 3 2 n - 1
+--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a)
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 3 2 3 2 n n - 1
+--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a)
+--R +
+--R 2 n 2
+--R 3x cos(n %pi)((- b x - a) )
+--R /
+--R 2 2 n 2
+--R (3sin(n %pi) + 3cos(n %pi) )((- b x - a) )
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=x*(a+b*x)^n/(-a-b*x)^n
+--R
+--R
+--R n
+--R x (b x + a)
+--R (1) ------------
+--R n
+--R (- b x - a)
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=1/2*x^2*(a+b*x)^n/(-a-b*x)^n
+--R
+--R
+--R 2 n
+--R x (b x + a)
+--R (2) -------------
+--R n
+--R 2(- b x - a)
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R x cos(n %pi)
+--R (3) ---------------------------
+--R 2 2
+--R 2sin(n %pi) + 2cos(n %pi)
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R 2 2 2 2 n 2 n
+--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a)
+--R (4) ----------------------------------------------------------------------
+--R 2 2 n
+--R (2sin(n %pi) + 2cos(n %pi) )(- b x - a)
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 n
+--R (- 2x sin(n %pi) - 2x cos(n %pi) )(- b x - a)
+--R +
+--R 2 2 2 2 n - 1
+--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a)
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 2 2 2 2 n n - 1
+--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a)
+--R +
+--R n 2
+--R 2x cos(n %pi)((- b x - a) )
+--R /
+--R 2 2 n 2
+--R (2sin(n %pi) + 2cos(n %pi) )((- b x - a) )
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(a+b*x)^n/(-a-b*x)^n
+--R
+--R
+--R n
+--R (b x + a)
+--R (1) ------------
+--R n
+--R (- b x - a)
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=x*(a+b*x)^n/(-a-b*x)^n
+--R
+--R
+--R n
+--R x (b x + a)
+--R (2) ------------
+--R n
+--R (- b x - a)
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R x cos(n %pi)
+--R (3) -------------------------
+--R 2 2
+--R sin(n %pi) + cos(n %pi)
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R 2 2 n n
+--R (- x sin(n %pi) - x cos(n %pi) )(b x + a) + x cos(n %pi)(- b x - a)
+--R (4) ----------------------------------------------------------------------
+--R 2 2 n
+--R (sin(n %pi) + cos(n %pi) )(- b x - a)
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 n
+--R (- sin(n %pi) - cos(n %pi) )(- b x - a)
+--R +
+--R 2 2 n - 1
+--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a)
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 2 2 n n - 1
+--R (- b n x sin(n %pi) - b n x cos(n %pi) )(- b x - a) (b x + a)
+--R +
+--R n 2
+--R cos(n %pi)((- b x - a) )
+--R /
+--R 2 2 n 2
+--R (sin(n %pi) + cos(n %pi) )((- b x - a) )
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(a+b*x)^n/(x*(-a-b*x)^n)
+--R
+--R
+--R n
+--R (b x + a)
+--R (1) --------------
+--R n
+--R x (- b x - a)
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=(a+b*x)^n*log(x)/(-a-b*x)^n
+--R
+--R
+--R n
+--R log(x)(b x + a)
+--R (2) ----------------
+--R n
+--R (- b x - a)
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R cos(n %pi)log(x)
+--R (3) -------------------------
+--R 2 2
+--R sin(n %pi) + cos(n %pi)
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 n
+--R (- log(x)sin(n %pi) - cos(n %pi) log(x))(b x + a)
+--R +
+--R n
+--R cos(n %pi)log(x)(- b x - a)
+--R /
+--R 2 2 n
+--R (sin(n %pi) + cos(n %pi) )(- b x - a)
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 n
+--R (- sin(n %pi) - cos(n %pi) )(- b x - a)
+--R +
+--R 2 2 n - 1
+--R (- b n x log(x)sin(n %pi) - b n x cos(n %pi) log(x))(- b x - a)
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 2 2 n
+--R (- b n x log(x)sin(n %pi) - b n x cos(n %pi) log(x))(- b x - a)
+--R *
+--R n - 1
+--R (b x + a)
+--R +
+--R n 2
+--R cos(n %pi)((- b x - a) )
+--R /
+--R 2 2 n 2
+--R (x sin(n %pi) + x cos(n %pi) )((- b x - a) )
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(a+b*x)^n/(x^2*(-a-b*x)^n)
+--R
+--R
+--R n
+--R (b x + a)
+--R (1) --------------
+--R 2 n
+--R x (- b x - a)
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=-(a+b*x)^n/(x*(-a-b*x)^n)
+--R
+--R
+--R n
+--R (b x + a)
+--R (2) - --------------
+--R n
+--R x (- b x - a)
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R cos(n %pi)
+--R (3) - -----------------------------
+--R 2 2
+--R x sin(n %pi) + x cos(n %pi)
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R 2 2 n n
+--R (sin(n %pi) + cos(n %pi) )(b x + a) - cos(n %pi)(- b x - a)
+--R (4) --------------------------------------------------------------
+--R 2 2 n
+--R (x sin(n %pi) + x cos(n %pi) )(- b x - a)
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 n
+--R (- sin(n %pi) - cos(n %pi) )(- b x - a)
+--R +
+--R 2 2 n - 1
+--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a)
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 2 2 n n - 1
+--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) (b x + a)
+--R +
+--R n 2
+--R cos(n %pi)((- b x - a) )
+--R /
+--R 2 2 2 2 n 2
+--R (x sin(n %pi) + x cos(n %pi) )((- b x - a) )
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(a+b*x)^n/(x^3*(-a-b*x)^n)
+--R
+--R
+--R n
+--R (b x + a)
+--R (1) --------------
+--R 3 n
+--R x (- b x - a)
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=-1/2*(a+b*x)^n/(x^2*(-a-b*x)^n)
+--R
+--R
+--R n
+--R (b x + a)
+--R (2) - ---------------
+--R 2 n
+--R 2x (- b x - a)
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R cos(n %pi)
+--R (3) - -------------------------------
+--R 2 2 2 2
+--R 2x sin(n %pi) + 2x cos(n %pi)
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R 2 2 n n
+--R (sin(n %pi) + cos(n %pi) )(b x + a) - cos(n %pi)(- b x - a)
+--R (4) --------------------------------------------------------------
+--R 2 2 2 2 n
+--R (2x sin(n %pi) + 2x cos(n %pi) )(- b x - a)
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 n
+--R (- 2sin(n %pi) - 2cos(n %pi) )(- b x - a)
+--R +
+--R 2 2 n - 1
+--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a)
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 2 2 n n - 1
+--R (b n x sin(n %pi) + b n x cos(n %pi) )(- b x - a) (b x + a)
+--R +
+--R n 2
+--R 2cos(n %pi)((- b x - a) )
+--R /
+--R 3 2 3 2 n 2
+--R (2x sin(n %pi) + 2x cos(n %pi) )((- b x - a) )
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(a+b*x)^n/(x^m*(-a-b*x)^n)
+--R
+--R
+--R n
+--R (b x + a)
+--R (1) --------------
+--R n m
+--R (- b x - a) x
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=x^(1-m)*(a+b*x)^n/((1-m)*(-a-b*x)^n)
+--R
+--R
+--R - m + 1 n
+--R x (b x + a)
+--R (2) - -------------------
+--R n
+--R (m - 1)(- b x - a)
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R x cos(n %pi)
+--R (3) - ---------------------------------------------------
+--R 2 2 m log(x)
+--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )%e
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 - m + 1 n m log(x)
+--R (sin(n %pi) + cos(n %pi) )x (b x + a) %e
+--R +
+--R n
+--R - x cos(n %pi)(- b x - a)
+--R /
+--R 2 2 n m log(x)
+--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )(- b x - a) %e
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 2 n - 1 - m + 1
+--R (b n sin(n %pi) + b n cos(n %pi) )(- b x - a) x
+--R +
+--R 2 2 n - m
+--R ((- m + 1)sin(n %pi) + (- m + 1)cos(n %pi) )(- b x - a) x
+--R *
+--R n
+--R (b x + a)
+--R +
+--R 2 2 n - m + 1 n - 1
+--R (b n sin(n %pi) + b n cos(n %pi) )(- b x - a) x (b x + a)
+--R *
+--R m log(x)
+--R %e
+--R +
+--R n 2
+--R (m - 1)cos(n %pi)((- b x - a) )
+--R /
+--R 2 2 n 2 m log(x)
+--R ((m - 1)sin(n %pi) + (m - 1)cos(n %pi) )((- b x - a) ) %e
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=x^3*sqrt(1+x)/(1-x)^(5/2)
+--R
+--R
+--R 3 +-----+
+--R x \|x + 1
+--R (1) -----------------------
+--R 2 +-------+
+--R (x - 2x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+11/2*asin(x)-6*sqrt(1+x)/sqrt(1-x)-_
+ 3*sqrt(1-x)*sqrt(1+x)-1/2*x*sqrt(1-x^2),11/2*asin(x)+2/3*x^3*_
+ sqrt(1+x)/(1-x)^(3/2)-13/3*x^2*sqrt(1+x)/sqrt(1-x)-13/3*sqrt(1-x)*_
+ sqrt(1+x)-1/6*(26+33*x)*sqrt(1-x)*sqrt(1+x)
+--R
+--R
+--R (2)
+--R [
+--R 2 +-----+
+--R (18x - 74x + 52)\|x + 1
+--R +
+--R +--------+
+--R 2 | 2 +-------+
+--R ((- 3x + 3x)\|- x + 1 + (33x - 33)asin(x))\|- x + 1
+--R /
+--R +-------+
+--R (6x - 6)\|- x + 1
+--R ,
+--R 3 2 +-----+ +-------+
+--R (3x + 12x - 71x + 52)\|x + 1 + (33x - 33)asin(x)\|- x + 1
+--R -------------------------------------------------------------]
+--R +-------+
+--R (6x - 6)\|- x + 1
+--R Type: Tuple(Expression(Integer))
+--E 222
+
+--S 223 of 500
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 500
+--m0:=a0-r0
+--E 224
+
+--S 225 of 500
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=x^2*sqrt(1+x)/(1-x)^(5/2)
+--R
+--R
+--R 2 +-----+
+--R x \|x + 1
+--R (1) -----------------------
+--R 2 +-------+
+--R (x - 2x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x)-4*sqrt(1+x)/sqrt(1-x)-_
+ sqrt(1-x)*sqrt(1+x),1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x)-_
+ 2*(1+x)^(3/2)/sqrt(1-x)-3*sqrt(1-x)*sqrt(1+x)
+--R
+--R
+--R (2)
+--R 2 +-----+ +-------+
+--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1
+--R [----------------------------------------------------,
+--R +-------+
+--R (3x - 3)\|- x + 1
+--R 2 +-----+ +-------+
+--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1
+--R ----------------------------------------------------]
+--R +-------+
+--R (3x - 3)\|- x + 1
+--R Type: Tuple(Expression(Integer))
+--E 227
+
+--S 228 of 500
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 500
+--m0:=a0-r0
+--E 229
+
+--S 230 of 500
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=x*sqrt(1+x)/(1-x)^(5/2)
+--R
+--R
+--R +-----+
+--R x\|x + 1
+--R (1) -----------------------
+--R 2 +-------+
+--R (x - 2x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x)-2*sqrt(1+x)/sqrt(1-x)
+--R
+--R
+--R +-----+ +-------+
+--R (- 7x + 5)\|x + 1 + (3x - 3)asin(x)\|- x + 1
+--R (2) ----------------------------------------------
+--R +-------+
+--R (3x - 3)\|- x + 1
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 500
+--m0:=a0-r0
+--E 234
+
+--S 235 of 500
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=sqrt(1+x)/(1-x)^(5/2)
+--R
+--R
+--R +-----+
+--R \|x + 1
+--R (1) -----------------------
+--R 2 +-------+
+--R (x - 2x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=1/3*(1+x)^(3/2)/(1-x)^(3/2)
+--R
+--R
+--R +-----+
+--R (- x - 1)\|x + 1
+--R (2) ------------------
+--R +-------+
+--R (3x - 3)\|- x + 1
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-----+ 2
+--R (8x + 8)\|- x + 1 \|x + 1 - 17x + 34x - 17
+--R (3) --------------------------------------------
+--R 2
+--R 24x - 48x + 24
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 17
+--R (4) - --
+--R 24
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=sqrt(1+x)/(-1+x)^(5/2)
+--R
+--R
+--R +-----+
+--R \|x + 1
+--R (1) ---------------------
+--R 2 +-----+
+--R (x - 2x + 1)\|x - 1
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=-1/3*(1+x)^(3/2)/(-1+x)^(3/2)
+--R
+--R
+--R +-----+
+--R (- x - 1)\|x + 1
+--R (2) -----------------
+--R +-----+
+--R (3x - 3)\|x - 1
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+ 2
+--R (- 3x - 3)\|x - 1 \|x + 1 + 4x - 8x + 4
+--R (3) -----------------------------------------
+--R 2
+--R 9x - 18x + 9
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4
+--R (4) -
+--R 9
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=sqrt(1+x)/((1-x)^(5/2)*x)
+--R
+--R
+--R +-----+
+--R \|x + 1
+--R (1) ------------------------
+--R 3 2 +-------+
+--R (x - 2x + x)\|- x + 1
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=-2*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/(1-x)^(3/2)+_
+ 5/3*sqrt(1+x)/sqrt(1-x)
+--R
+--R
+--R +-------+
+--R +-------+ \|- x + 1 +-----+
+--R (- 6x + 6)\|- x + 1 atanh(----------) + (5x - 7)\|x + 1
+--R +-----+
+--R \|x + 1
+--R (2) --------------------------------------------------------
+--R +-------+
+--R (3x - 3)\|- x + 1
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-----+
+--R 2 - \|- x + 1 \|x + 1 - 1
+--R (- 3x + 6x - 3)log(------------------------)
+--R x
+--R +
+--R +-------+ +-----+ 2
+--R (- 5x + 7)\|- x + 1 \|x + 1 - 3x + 6x - 3
+--R /
+--R 2
+--R 3x - 6x + 3
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-----+ +-------+
+--R - \|- x + 1 \|x + 1 - 1 \|- x + 1
+--R (4) - log(------------------------) + 2atanh(----------) - 1
+--R x +-----+
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=sqrt(1+x)/((1-x)^(5/2)*x^2)
+--R
+--R
+--R +-----+
+--R \|x + 1
+--R (1) -------------------------
+--R 4 3 2 +-------+
+--R (x - 2x + x )\|- x + 1
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=-6*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x)+_
+ 3*sqrt(1+x)/(x*sqrt(1-x))-14/3*sqrt(1-x)*sqrt(1+x)/x
+--R
+--R
+--R +-------+
+--R 2 +-------+ \|- x + 1 2 +-----+
+--R (- 18x + 18x)\|- x + 1 atanh(----------) + (14x - 19x + 3)\|x + 1
+--R +-----+
+--R \|x + 1
+--R (2) --------------------------------------------------------------------
+--R 2 +-------+
+--R (3x - 3x)\|- x + 1
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-----+
+--R 3 2 \|- x + 1 \|x + 1 + 1
+--R (- 144x + 288x - 144x)log(----------------------)
+--R x
+--R +
+--R 2 +-------+ +-----+ 3 2
+--R (- 224x + 304x - 48)\|- x + 1 \|x + 1 + 273x - 546x + 273x
+--R /
+--R 3 2
+--R 48x - 96x + 48x
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-----+ +-------+
+--R \|- x + 1 \|x + 1 + 1 \|- x + 1
+--R - 48log(----------------------) + 96atanh(----------) + 91
+--R x +-----+
+--R \|x + 1
+--R (4) ----------------------------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=sqrt(1+x)/((1-x)^(5/2)*x^3)
+--R
+--R
+--R +-----+
+--R \|x + 1
+--R (1) -------------------------
+--R 5 4 3 +-------+
+--R (x - 2x + x )\|- x + 1
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=-11*atanh(sqrt(1-x)/sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x^2)+_
+ 13/3*sqrt(1+x)/(x^2*sqrt(1-x))-11/2*sqrt(1-x)*sqrt(1+x)/x^2-_
+ 26/3*sqrt(1-x)*sqrt(1+x)/x
+--R
+--R
+--R (2)
+--R +-------+
+--R 3 2 +-------+ \|- x + 1 3 2 +-----+
+--R (- 66x + 66x )\|- x + 1 atanh(----------) + (52x - 71x + 12x + 3)\|x + 1
+--R +-----+
+--R \|x + 1
+--R ----------------------------------------------------------------------------
+--R 3 2 +-------+
+--R (6x - 6x )\|- x + 1
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-----+
+--R 4 3 2 - \|- x + 1 \|x + 1 - 1
+--R (- 528x + 1056x - 528x )log(------------------------)
+--R x
+--R +
+--R 3 2 +-------+ +-----+ 4 3 2
+--R (- 832x + 1136x - 192x - 48)\|- x + 1 \|x + 1 - 159x + 318x - 159x
+--R /
+--R 4 3 2
+--R 96x - 192x + 96x
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-----+ +-------+
+--R - \|- x + 1 \|x + 1 - 1 \|- x + 1
+--R - 176log(------------------------) + 352atanh(----------) - 53
+--R x +-----+
+--R \|x + 1
+--R (4) --------------------------------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=x^2/(sqrt(-1+x)*sqrt(1+x))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=1/2*acosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R +-----+ +-----+
+--R x\|x - 1 \|x + 1 + acosh(x)
+--R (2) ----------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+ +-----+ +-----+
+--R - log(\|x - 1 \|x + 1 - x) + x\|x - 1 \|x + 1
+--R (3) -----------------------------------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+
+--R - log(\|x - 1 \|x + 1 - x) - acosh(x)
+--R (4) --------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R +------+
+--R | 2 +-----+ +-----+
+--R \|x - 1 - \|x - 1 \|x + 1
+--R (5) ----------------------------
+--R +------+
+--R +-----+ +-----+ | 2
+--R 2\|x - 1 \|x + 1 \|x - 1
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=x/(sqrt(-1+x)*sqrt(1+x))
+--R
+--R
+--R x
+--R (1) ----------------
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R +-----+ +-----+
+--R (2) \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+
+--R (3) \|x - 1 \|x + 1
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=1/(sqrt(-1+x)*sqrt(1+x))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=acosh(x)
+--R
+--R
+--R (2) acosh(x)
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+
+--R (3) - log(- \|x - 1 \|x + 1 + x)
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+
+--R (4) - log(- \|x - 1 \|x + 1 + x) - acosh(x)
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R +------+
+--R | 2 +-----+ +-----+
+--R \|x - 1 - \|x - 1 \|x + 1
+--R (5) ----------------------------
+--R +------+
+--R +-----+ +-----+ | 2
+--R \|x - 1 \|x + 1 \|x - 1
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=1/(x*sqrt(-1+x)*sqrt(1+x))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R +-----+ +-----+
+--R x\|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=2*atan(sqrt(-1+x)/sqrt(1+x))
+--R
+--R
+--R +-----+
+--R \|x - 1
+--R (2) 2atan(--------)
+--R +-----+
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+
+--R 16\|x - 1 \|x + 1 - 63
+--R (3) atan(-----------------------)
+--R +-----+ +-----+
+--R 63\|x - 1 \|x + 1 + 16
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+ +-----+
+--R 16\|x - 1 \|x + 1 - 63 \|x - 1
+--R (4) atan(-----------------------) - 2atan(--------)
+--R +-----+ +-----+ +-----+
+--R 63\|x - 1 \|x + 1 + 16 \|x + 1
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=1/(x^2*sqrt(-1+x)*sqrt(1+x))
+--R
+--R
+--R 1
+--R (1) ------------------
+--R 2 +-----+ +-----+
+--R x \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=sqrt(-1+x)*sqrt(1+x)/x
+--R
+--R
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R (2) ----------------
+--R x
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1 + x
+--R (3) --------------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4) 1
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=x^2*sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R 2 +-----+ +-----+
+--R (1) x \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=-1/8*acosh(x)-1/8*x*sqrt(-1+x)*sqrt(1+x)+1/4*x^3*sqrt(-1+x)*_
+ sqrt(1+x),1/4*(-1+x)^(3/2)*x*(1+x)^(3/2)-1/8*acosh(x)+_
+ 1/8*(-1+x)^(3/2)*sqrt(1+x)+1/8*sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R (2)
+--R 3 +-----+ +-----+ 3 +-----+ +-----+
+--R (2x - x)\|x - 1 \|x + 1 - acosh(x) (2x - x)\|x - 1 \|x + 1 - acosh(x)
+--R [------------------------------------,------------------------------------]
+--R 8 8
+--R Type: Tuple(Expression(Integer))
+--E 287
+
+--S 288 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+ 3 +-----+ +-----+
+--R - log(- \|x - 1 \|x + 1 - x) + (2x - x)\|x - 1 \|x + 1
+--R (3) ---------------------------------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+
+--R - log(- \|x - 1 \|x + 1 - x) + acosh(x)
+--R (4) ----------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R +------+
+--R | 2 +-----+ +-----+
+--R - \|x - 1 + \|x - 1 \|x + 1
+--R (5) ------------------------------
+--R +------+
+--R +-----+ +-----+ | 2
+--R 8\|x - 1 \|x + 1 \|x - 1
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=x*sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R +-----+ +-----+
+--R (1) x\|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=1/3*(-1+x)^(3/2)*(1+x)^(3/2)
+--R
+--R
+--R 2 +-----+ +-----+
+--R (x - 1)\|x - 1 \|x + 1
+--R (2) ------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-----+ +-----+
+--R (x - 1)\|x - 1 \|x + 1
+--R (3) ------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R +-----+ +-----+
+--R (1) \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=-1/2*acosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x),_
+ -1/2*acosh(x)+1/2*(-1+x)^(3/2)*sqrt(1+x)+1/2*sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R +-----+ +-----+ +-----+ +-----+
+--R x\|x - 1 \|x + 1 - acosh(x) x\|x - 1 \|x + 1 - acosh(x)
+--R (2) [----------------------------,----------------------------]
+--R 2 2
+--R Type: Tuple(Expression(Integer))
+--E 297
+
+--S 298 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+ +-----+ 2 +-----+ +-----+
+--R (- 4x\|x - 1 \|x + 1 - 4x + 2)log(\|x + 1 + \|x - 1 )
+--R +
+--R 3 +-----+ +-----+ 4 2
+--R (2x - x)\|x - 1 \|x + 1 + 2x - 2x
+--R /
+--R +-----+ +-----+ 2
+--R 4x\|x - 1 \|x + 1 + 4x - 2
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+
+--R - 2log(\|x + 1 + \|x - 1 ) + acosh(x)
+--R (4) --------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R +------+
+--R | 2 +-----+ +-----+
+--R - \|x - 1 + \|x - 1 \|x + 1
+--R (5) ------------------------------
+--R +------+
+--R +-----+ +-----+ | 2
+--R 2\|x - 1 \|x + 1 \|x - 1
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=sqrt(-1+x)*sqrt(1+x)/x
+--R
+--R
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R (1) ----------------
+--R x
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=-2*atan(sqrt(-1+x)/sqrt(1+x))+sqrt(-1+x)*sqrt(1+x)
+--R
+--R
+--R +-----+
+--R \|x - 1 +-----+ +-----+
+--R (2) - 2atan(--------) + \|x - 1 \|x + 1
+--R +-----+
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+
+--R 16\|x - 1 \|x + 1 - 63 +-----+ +-----+
+--R (3) - atan(-----------------------) + \|x - 1 \|x + 1
+--R +-----+ +-----+
+--R 63\|x - 1 \|x + 1 + 16
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+ +-----+
+--R 16\|x - 1 \|x + 1 - 63 \|x - 1
+--R (4) - atan(-----------------------) + 2atan(--------)
+--R +-----+ +-----+ +-----+
+--R 63\|x - 1 \|x + 1 + 16 \|x + 1
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=sqrt(-1+x)*sqrt(1+x)/x^2
+--R
+--R
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R (1) ----------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=acosh(x)-sqrt(-1+x)*sqrt(1+x)/x
+--R
+--R
+--R +-----+ +-----+
+--R - \|x - 1 \|x + 1 + x acosh(x)
+--R (2) -------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-----+ +-----+ +-----+ +-----+
+--R - x log(\|x - 1 \|x + 1 - x) - \|x - 1 \|x + 1 + x
+--R (3) ----------------------------------------------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+
+--R (4) - log(\|x - 1 \|x + 1 - x) - acosh(x) + 1
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R +------+
+--R | 2 +-----+ +-----+
+--R \|x - 1 - \|x - 1 \|x + 1
+--R (5) ----------------------------
+--R +------+
+--R +-----+ +-----+ | 2
+--R \|x - 1 \|x + 1 \|x - 1
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=1/(sqrt(1+2*x)*sqrt(3+2*x))
+--R
+--R
+--R 1
+--R (1) ------------------
+--R +------+ +------+
+--R \|2x + 1 \|2x + 3
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=asinh(sqrt(1+2*x)/sqrt(2))
+--R
+--R
+--R +------+
+--R \|2x + 1
+--R (2) asinh(---------)
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+
+--R log(- \|2x + 1 \|2x + 3 + 2x + 2)
+--R (3) - ----------------------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R +------+ +------+ \|2x + 1
+--R - log(- \|2x + 1 \|2x + 3 + 2x + 2) - 2asinh(---------)
+--R +-+
+--R \|2
+--R (4) --------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=1/(x*sqrt(-2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +------+ +------+
+--R x\|3x - 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=atan(sqrt(3/2)*sqrt(-2+3*x)/sqrt(3+5*x))*sqrt(2/3)
+--R
+--R
+--R +-+ +------+
+--R +-+ \|3 \|3x - 2
+--R \|2 atan(-------------)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R (2) -----------------------
+--R +-+
+--R \|3
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+ +------+ +------+ +-+ +-+
+--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (- 337x - 4044)\|2 \|3
+--R \|2 \|3 atan(-------------------------------------------------------)
+--R +------+ +------+
+--R 4044\|3x - 2 \|5x + 3 + 456x + 5472
+--R (3) ---------------------------------------------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +------+ +------+ +-+ +-+
+--R +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (- 337x - 4044)\|2 \|3
+--R \|2 atan(-------------------------------------------------------)
+--R +------+ +------+
+--R 4044\|3x - 2 \|5x + 3 + 456x + 5472
+--R +
+--R +-+ +------+
+--R +-+ \|3 \|3x - 2
+--R - 2\|2 atan(-------------)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R /
+--R +-+
+--R 2\|3
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=1/((-1+x)^(3/2)*x*(1+x)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R 3 +-----+ +-----+
+--R (x - x)\|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=-2*atan(sqrt(-1+x)/sqrt(1+x))+(-1)/(sqrt(-1+x)*sqrt(1+x))
+--R
+--R
+--R +-----+
+--R +-----+ +-----+ \|x - 1
+--R - 2\|x - 1 \|x + 1 atan(--------) - 1
+--R +-----+
+--R \|x + 1
+--R (2) -------------------------------------
+--R +-----+ +-----+
+--R \|x - 1 \|x + 1
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500 ok to fail. differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+ +-----+
+--R 2 16\|x - 1 \|x + 1 - 63 +-----+ +-----+ 2
+--R (- 12x + 12)atan(-----------------------) - 12\|x - 1 \|x + 1 - 7x + 7
+--R +-----+ +-----+
+--R 63\|x - 1 \|x + 1 + 16
+--R -------------------------------------------------------------------------
+--R 2
+--R 12x - 12
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500 ok to fail. differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-----+ +-----+ +-----+
+--R 16\|x - 1 \|x + 1 - 63 \|x - 1
+--R - 12atan(-----------------------) + 24atan(--------) - 7
+--R +-----+ +-----+ +-----+
+--R 63\|x - 1 \|x + 1 + 16 \|x + 1
+--R (4) --------------------------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=x*sqrt(1-x)*sqrt(1+x)
+--R
+--R
+--R +-------+ +-----+
+--R (1) x\|- x + 1 \|x + 1
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=-1/3*(1-x)^(3/2)*(1+x)^(3/2)
+--R
+--R
+--R 2 +-------+ +-----+
+--R (x - 1)\|- x + 1 \|x + 1
+--R (2) --------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-------+ +-----+
+--R (x - 1)\|- x + 1 \|x + 1
+--R (3) --------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=x^3*(2+3*x)^(3/2)*(1+4*x)^(1/2)
+--R
+--R
+--R 4 3 +------+ +------+
+--R (1) (3x + 2x )\|3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=22357/6635520*(2+3*x)^(3/2)*(1+4*x)^(3/2)+1/92160*(8-403*x)*_
+ (2+3*x)^(3/2)*(1+4*x)^(3/2)-1/960*x^2*(2+3*x)^(3/2)*(1+4*x)^(3/2)+_
+ 1/24*x^3*(2+3*x)^(3/2)*(1+4*x)^(3/2)+1067875/84934656*_
+ asinh(sqrt(3/5)*sqrt(1+4*x))/sqrt(3)-42715/5308416*(2+3*x)^(3/2)*_
+ sqrt(1+4*x)+213575/42467328*sqrt(2+3*x)*sqrt(1+4*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|3 \|4x + 1
+--R 5339375asinh(-------------)
+--R +-+
+--R \|5
+--R +
+--R 5 4 3 2
+--R 212336640x + 189333504x + 8239104x - 3699456x + 2179184x
+--R +
+--R - 1763226
+--R *
+--R +-+ +------+ +------+
+--R \|3 \|3x + 2 \|4x + 1
+--R /
+--R +-+
+--R 424673280\|3
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 500
+--m0:=a0-r0
+--E 334
+
+--S 335 of 500
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=1/(sqrt(-1+a+b*x)*sqrt(1+a+b*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +-----------+ +-----------+
+--R \|b x + a - 1 \|b x + a + 1
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=2*asinh(sqrt(-1+a+b*x)/sqrt(2))/b
+--R
+--R
+--R +-----------+
+--R \|b x + a - 1
+--R 2asinh(--------------)
+--R +-+
+--R \|2
+--R (2) ----------------------
+--R b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 500
+--m0:=a0-r0
+--E 339
+
+--S 340 of 500
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=x^2*(1+x)^(1/4)/(1-x)^(1/4)
+--R
+--R
+--R 2 4+-----+
+--R x \|x + 1
+--R (1) ----------
+--R 4+-------+
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=-3/8*(1-x)^(3/4)*(1+x)^(1/4)-1/12*(1-x)^(3/4)*(1+x)^(5/4)-_
+ 1/3*(1-x)^(3/4)*x*(1+x)^(5/4)+3/8*atan(1-(1-x)^(1/4)*sqrt(2)/_
+ (1+x)^(1/4))/sqrt(2)-3/8*atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/_
+ sqrt(2)-3/16*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/_
+ sqrt(1+x))/sqrt(2)+3/16*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+_
+ sqrt(1-x)/sqrt(1+x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+
+--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1
+--R 9log(--------------------------------------------------------)
+--R +-----+4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+
+--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1
+--R - 9log(--------------------------------------------------------)
+--R +-----+4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+
+--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1
+--R - 18atan(-------------------------) + 18atan(-------------------------)
+--R 4+-----+ 4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R 2 +-+4+-------+3 4+-----+
+--R (- 16x - 20x - 22)\|2 \|- x + 1 \|x + 1
+--R /
+--R +-+
+--R 48\|2
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 500
+--m0:=a0-r0
+--E 344
+
+--S 345 of 500
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=x*(1+x)^(1/4)/(1-x)^(1/4)
+--R
+--R
+--R 4+-----+
+--R x\|x + 1
+--R (1) ----------
+--R 4+-------+
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=-1/4*(1-x)^(3/4)*(1+x)^(1/4)-1/2*(1-x)^(3/4)*(1+x)^(5/4)+_
+ 1/4*atan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_
+ 1/4*atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_
+ 1/8*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/_
+ sqrt(2)+1/8*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+_
+ sqrt(1-x)/sqrt(1+x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+
+--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1
+--R log(--------------------------------------------------------)
+--R +-----+4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+
+--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1
+--R - log(--------------------------------------------------------)
+--R +-----+4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+
+--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1
+--R - 2atan(-------------------------) + 2atan(-------------------------)
+--R 4+-----+ 4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R +-+4+-------+3 4+-----+
+--R (- 4x - 6)\|2 \|- x + 1 \|x + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+--a0:=integrate(t0,x)
+--E 348
+
+--S 349 of 500
+--m0:=a0-r0
+--E 349
+
+--S 350 of 500
+--d0:=D(m0,x)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1+x)^(1/4)/(1-x)^(1/4)
+--R
+--R
+--R 4+-----+
+--R \|x + 1
+--R (1) ----------
+--R 4+-------+
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=-(1-x)^(3/4)*(1+x)^(1/4)+atan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/_
+ sqrt(2)-atan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-_
+ 1/2*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/_
+ sqrt(2)+1/2*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/_
+ sqrt(1+x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+
+--R (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1
+--R log(--------------------------------------------------------)
+--R +-----+4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+
+--R (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1
+--R - log(--------------------------------------------------------)
+--R +-----+4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R 4+-----+ +-+4+-------+ 4+-----+ +-+4+-------+
+--R \|x + 1 + \|2 \|- x + 1 \|x + 1 - \|2 \|- x + 1
+--R - 2atan(-------------------------) + 2atan(-------------------------)
+--R 4+-----+ 4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R +-+4+-------+3 4+-----+
+--R - 2\|2 \|- x + 1 \|x + 1
+--R /
+--R +-+
+--R 2\|2
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1+x)^(1/4)/((1-x)^(1/4)*x)
+--R
+--R
+--R 4+-----+
+--R \|x + 1
+--R (1) -----------
+--R 4+-------+
+--R x\|- x + 1
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=-2*atan((1+x)^(1/4)/(1-x)^(1/4))-2*atanh((1+x)^(1/4)/(1-x)^(1/4))-_
+ log(1-(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4)+sqrt(1+x)/sqrt(1-x))/_
+ sqrt(2)+log(1+(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4)+sqrt(1+x)/_
+ sqrt(1-x))/sqrt(2)-atan(1-(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4))*_
+ sqrt(2)+atan(1+(1+x)^(1/4)*sqrt(2)/(1-x)^(1/4))*sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ +-------+4+-----+ 4+-------+ +-----+ +-------+4+-------+
+--R \|2 \|- x + 1 \|x + 1 + \|- x + 1 \|x + 1 + \|- x + 1 \|- x + 1
+--R log(------------------------------------------------------------------)
+--R +-------+4+-------+
+--R \|- x + 1 \|- x + 1
+--R +
+--R -
+--R log
+--R +-+ +-------+4+-----+ 4+-------+ +-----+
+--R - \|2 \|- x + 1 \|x + 1 + \|- x + 1 \|x + 1
+--R +
+--R +-------+4+-------+
+--R \|- x + 1 \|- x + 1
+--R /
+--R +-------+4+-------+
+--R \|- x + 1 \|- x + 1
+--R +
+--R 4+-----+ +-+4+-----+ 4+-------+
+--R +-+ \|x + 1 \|2 \|x + 1 + \|- x + 1
+--R - 2\|2 atanh(----------) + 2atan(-------------------------)
+--R 4+-------+ 4+-------+
+--R \|- x + 1 \|- x + 1
+--R +
+--R +-+4+-----+ 4+-------+ 4+-----+
+--R \|2 \|x + 1 - \|- x + 1 +-+ \|x + 1
+--R 2atan(-------------------------) - 2\|2 atan(----------)
+--R 4+-------+ 4+-------+
+--R \|- x + 1 \|- x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 500
+--m0:=a0-r0
+--E 359
+
+--S 360 of 500
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^2)
+--R
+--R
+--R 4+-----+
+--R \|x + 1
+--R (1) ------------
+--R 2 4+-------+
+--R x \|- x + 1
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=-(1-x)^(3/4)*(1+x)^(1/4)/x+atan((1-x)^(1/4)/(1+x)^(1/4))-_
+ atanh((1-x)^(1/4)/(1+x)^(1/4))
+--R
+--R
+--R 4+-------+ 4+-------+
+--R \|- x + 1 \|- x + 1 4+-------+3 4+-----+
+--R - x atanh(----------) + x atan(----------) - \|- x + 1 \|x + 1
+--R 4+-----+ 4+-----+
+--R \|x + 1 \|x + 1
+--R (2) ----------------------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 500
+--m0:=a0-r0
+--E 364
+
+--S 365 of 500
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^3)
+--R
+--R
+--R 4+-----+
+--R \|x + 1
+--R (1) ------------
+--R 3 4+-------+
+--R x \|- x + 1
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=-1/2*(1-x)^(3/4)*(1+x)^(1/4)/x^2-3/4*(1-x)^(3/4)*(1+x)^(1/4)/x+_
+ 1/4*atan((1-x)^(1/4)/(1+x)^(1/4))-1/4*atanh((1-x)^(1/4)/(1+x)^(1/4))
+--R
+--R
+--R (2)
+--R 4+-------+ 4+-------+
+--R 2 \|- x + 1 2 \|- x + 1 4+-------+3 4+-----+
+--R - x atanh(----------) + x atan(----------) + (- 3x - 2)\|- x + 1 \|x + 1
+--R 4+-----+ 4+-----+
+--R \|x + 1 \|x + 1
+--R --------------------------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1+x)^(1/4)/((1-x)^(1/4)*x^4)
+--R
+--R
+--R 4+-----+
+--R \|x + 1
+--R (1) ------------
+--R 4 4+-------+
+--R x \|- x + 1
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=-1/3*(1-x)^(3/4)*(1+x)^(1/4)/x^3-5/12*(1-x)^(3/4)*(1+x)^(1/4)/x^2-_
+ 11/24*(1-x)^(3/4)*(1+x)^(1/4)/x+3/8*atan((1-x)^(1/4)/(1+x)^(1/4))-_
+ 3/8*atanh((1-x)^(1/4)/(1+x)^(1/4))
+--R
+--R
+--R (2)
+--R 4+-------+ 4+-------+
+--R 3 \|- x + 1 3 \|- x + 1
+--R - 9x atanh(----------) + 9x atan(----------)
+--R 4+-----+ 4+-----+
+--R \|x + 1 \|x + 1
+--R +
+--R 2 4+-------+3 4+-----+
+--R (- 11x - 10x - 8)\|- x + 1 \|x + 1
+--R /
+--R 3
+--R 24x
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=x^3*(a+b*x)^(1/4)/(c+d*x)^(1/4)
+--R
+--R
+--R 3 4+-------+
+--R x \|b x + a
+--R (1) ------------
+--R 4+-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=-1/1536*(585*b^3*c^3-63*a*b^2*c^2*d-61*a^2*b*c*d^2-77*a^3*d^3)*_
+ (a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^4)-1/384*(10*a*c-_
+ 117*b*c^2/d+11*a^2*d/b)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)-_
+ 1/48*(13*b*c-a*d)*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+_
+ 1/4*x^3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/d+1/1024*(b*c-a*d)*_
+ (195*b^3*c^3+135*a*b^2*c^2*d+105*a^2*b*c*d^2+77*a^3*d^3)*_
+ atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*_
+ d^(17/4))+1/1024*(b*c-a*d)*(195*b^3*c^3+135*a*b^2*c^2*d+_
+ 105*a^2*b*c*d^2+77*a^3*d^3)*atanh(d^(1/4)*(a+b*x)^(1/4)/_
+ (b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(17/4))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 231a d - 84a b c d - 90a b c d - 180a b c d + 585b c )
+--R *
+--R 4+-+4+-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 231a d - 84a b c d - 90a b c d - 180a b c d + 585b c )
+--R *
+--R 4+-+4+-------+
+--R \|d \|b x + a
+--R atan(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 768b d x + (64a b d - 832b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2
+--R (- 88a b d - 80a b c d + 936b c d)x + 154a d + 122a b c d
+--R +
+--R 2 2 3 3
+--R 126a b c d - 1170b c
+--R *
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 4 4+-+3 4+-+
+--R 3072b d \|b \|d
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=x^2*(a+b*x)^(1/4)/(c+d*x)^(1/4)
+--R
+--R
+--R 2 4+-------+
+--R x \|b x + a
+--R (1) ------------
+--R 4+-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=1/32*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_
+ (b^2*d^3)-1/24*(9*b*c+7*a*d)*(a+b*x)^(5/4)*(c+d*x)^(3/4)/_
+ (b^2*d^2)+1/3*x*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)-1/64*_
+ (b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*atan(d^(1/4)*_
+ (a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4))-_
+ 1/64*(b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*_
+ atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (21a d + 9a b c d + 15a b c d - 45b c )atanh(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (21a d + 9a b c d + 15a b c d - 45b c )atan(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 4+-+3
+--R (64b d x + (8a b d - 72b c d)x - 14a d - 12a b c d + 90b c )\|b
+--R *
+--R 4+-+4+-------+4+-------+3
+--R \|d \|b x + a \|d x + c
+--R /
+--R 2 3 4+-+3 4+-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 500
+--m0:=a0-r0
+--E 384
+
+--S 385 of 500
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=x*(a+b*x)^(1/4)/(c+d*x)^(1/4)
+--R
+--R
+--R 4+-------+
+--R x\|b x + a
+--R (1) -----------
+--R 4+-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=-1/8*(5*b*c+3*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+_
+ 1/2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)+1/16*(b*c-a*d)*_
+ (5*b*c+3*a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_
+ (b^(7/4)*d^(9/4))+1/16*(b*c-a*d)*(5*b*c+3*a*d)*_
+ atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(9/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (- 3a d - 2a b c d + 5b c )atanh(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (- 3a d - 2a b c d + 5b c )atan(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R (8b d x + 2a d - 10b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 4+-+3 4+-+
+--R 16b d \|b \|d
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 500
+--m0:=a0-r0
+--E 389
+
+--S 390 of 500
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(a+b*x)^(1/4)/(c+d*x)^(1/4)
+--R
+--R
+--R 4+-------+
+--R \|b x + a
+--R (1) ----------
+--R 4+-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=(a+b*x)^(1/4)*(c+d*x)^(3/4)/d-1/2*(b*c-a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/_
+ (b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4))-1/2*(b*c-a*d)*_
+ atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|d \|b x + a \|d \|b x + a
+--R (a d - b c)atanh(--------------) + (a d - b c)atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|b \|d x + c \|b \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R 2\|b \|d \|b x + a \|d x + c
+--R /
+--R 4+-+3 4+-+
+--R 2d \|b \|d
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 500
+--m0:=a0-r0
+--E 394
+
+--S 395 of 500
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(a+b*x)^(1/4)/(x*(c+d*x)^(1/4))
+--R
+--R
+--R 4+-------+
+--R \|b x + a
+--R (1) -----------
+--R 4+-------+
+--R x\|d x + c
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=-2*a^(1/4)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+_
+ 2*b^(1/4)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4)-_
+ 2*a^(1/4)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+_
+ 2*b^(1/4)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4)
+--R
+--R
+--R (2)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R 4+-+4+-+ \|d \|b x + a 4+-+4+-+ \|c \|b x + a
+--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|b \|d x + c \|a \|d x + c
+--R +
+--R 4+-+4+-------+ 4+-+4+-------+
+--R 4+-+4+-+ \|d \|b x + a 4+-+4+-+ \|c \|b x + a
+--R 2\|b \|c atan(--------------) - 2\|a \|d atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|b \|d x + c \|a \|d x + c
+--R /
+--R 4+-+4+-+
+--R \|c \|d
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 500
+--m0:=a0-r0
+--E 399
+
+--S 400 of 500
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(a+b*x)^(1/4)/(x^2*(c+d*x)^(1/4))
+--R
+--R
+--R 4+-------+
+--R \|b x + a
+--R (1) ------------
+--R 2 4+-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x)-1/2*(b*c-a*d)*_
+ atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(5/4))-_
+ 1/2*(b*c-a*d)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(3/4)*c^(5/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|c \|b x + a \|c \|b x + a
+--R (a d - b c)x atanh(--------------) + (a d - b c)x atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|a \|d x + c \|a \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R - 2\|a \|c \|b x + a \|d x + c
+--R /
+--R 4+-+3 4+-+
+--R 2c x \|a \|c
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 500
+--m0:=a0-r0
+--E 404
+
+--S 405 of 500
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(a+b*x)^(1/4)/(x^3*(c+d*x)^(1/4))
+--R
+--R
+--R 4+-------+
+--R \|b x + a
+--R (1) ------------
+--R 3 4+-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^2)-1/8*(b*c-5*a*d)*(a+b*x)^(1/4)*_
+ (c+d*x)^(3/4)/(a*c^2*x)+1/16*(b*c-a*d)*(3*b*c+5*a*d)*_
+ atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(7/4)*c^(9/4))+1/16*(b*c-a*d)*(3*b*c+5*a*d)*atanh(c^(1/4)*_
+ (a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(9/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 5a d + 2a b c d + 3b c )x atanh(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 5a d + 2a b c d + 3b c )x atan(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R ((10a d - 2b c)x - 8a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 4+-+3 4+-+
+--R 16a c x \|a \|c
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 500
+--m0:=a0-r0
+--E 409
+
+--S 410 of 500
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(a+b*x)^(1/4)/(x^4*(c+d*x)^(1/4))
+--R
+--R
+--R 4+-------+
+--R \|b x + a
+--R (1) ------------
+--R 4 4+-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^3)-1/24*(b*c-9*a*d)*(a+b*x)^(1/4)*_
+ (c+d*x)^(3/4)/(a*c^2*x^2)+1/96*(7*b*c-15*a*d)*(b*c+3*a*d)*_
+ (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^3*x)-1/64*(b*c-a*d)*_
+ (7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*atan(c^(1/4)*(a+b*x)^(1/4)/_
+ (a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4))-1/64*(b*c-a*d)*_
+ (7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*atanh(c^(1/4)*(a+b*x)^(1/4)/_
+ (a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (45a d - 15a b c d - 9a b c d - 21b c )x atanh(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (45a d - 15a b c d - 9a b c d - 21b c )x atan(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2
+--R ((- 90a d + 12a b c d + 14b c )x + (72a c d - 8a b c )x - 64a c )
+--R *
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 3 3 4+-+3 4+-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 500
+--m0:=a0-r0
+--E 414
+
+--S 415 of 500
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(a+b*x)^(1/4)/(x^5*(c+d*x)^(1/4))
+--R
+--R
+--R 4+-------+
+--R \|b x + a
+--R (1) ------------
+--R 5 4+-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=-1/4*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^4)-1/48*(b*c-13*a*d)*_
+ (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c^2*x^3)+1/384*(11*b^2*c^2+_
+ 10*a*b*c*d-117*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_
+ (a^2*c^3*x^2)-1/1536*(77*b^3*c^3+61*a*b^2*c^2*d+63*a^2*b*c*d^2-_
+ 585*a^3*d^3)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^3*c^4*x)+_
+ 1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+135*a^2*b*c*d^2+_
+ 195*a^3*d^3)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(15/4)*c^(17/4))+1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+_
+ 135*a^2*b*c*d^2+195*a^3*d^3)*atanh(c^(1/4)*(a+b*x)^(1/4)/_
+ (a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(17/4))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 585a d + 180a b c d + 90a b c d + 84a b c d + 231b c )x
+--R *
+--R 4+-+4+-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 585a d + 180a b c d + 90a b c d + 84a b c d + 231b c )x
+--R *
+--R 4+-+4+-------+
+--R \|c \|b x + a
+--R atan(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (1170a d - 126a b c d - 122a b c d - 154b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 936a c d + 80a b c d + 88a b c )x + (832a c d - 64a b c )x
+--R +
+--R 3 3
+--R - 768a c
+--R *
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 4 4 4+-+3 4+-+
+--R 3072a c x \|a \|c
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=x^4/((a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R 4+-------+3 4+-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=-1/1536*(585*b^3*c^3+657*a*b^2*c^2*d+803*a^2*b*c*d^2+1155*a^3*d^3)*_
+ (a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^4*d^4)+1/384*(117*b^2*c^2+_
+ 134*a*b*c*d+165*a^2*d^2)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^3)-_
+ 1/48*(13*b*c+15*a*d)*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+_
+ 1/4*x^3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/1024*(195*b^4*c^4+_
+ 180*a*b^3*c^3*d+210*a^2*b^2*c^2*d^2+308*a^3*b*c*d^3+1155*a^4*d^4)*_
+ atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(19/4)*d^(17/4))+_
+ 1/1024*(195*b^4*c^4+180*a*b^3*c^3*d+210*a^2*b^2*c^2*d^2+_
+ 308*a^3*b*c*d^3+1155*a^4*d^4)*atanh(d^(1/4)*(a+b*x)^(1/4)/_
+ (b^(1/4)*(c+d*x)^(1/4)))/(b^(19/4)*d^(17/4))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (3465a d + 924a b c d + 630a b c d + 540a b c d + 585b c )
+--R *
+--R 4+-+4+-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (3465a d + 924a b c d + 630a b c d + 540a b c d + 585b c )
+--R *
+--R 4+-+4+-------+
+--R \|d \|b x + a
+--R atan(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 768b d x + (- 960a b d - 832b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2
+--R (1320a b d + 1072a b c d + 936b c d)x - 2310a d - 1606a b c d
+--R +
+--R 2 2 3 3
+--R - 1314a b c d - 1170b c
+--R *
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 4 4+-+3 4+-+
+--R 3072b d \|b \|d
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=x^3/((a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R 4+-------+3 4+-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=1/96*(45*b^2*c^2+54*a*b*c*d+77*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_
+ (b^3*d^3)-1/24*(9*b*c+11*a*d)*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_
+ (b^2*d^2)+1/3*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-_
+ 1/64*(15*b^3*c^3+15*a*b^2*c^2*d+21*a^2*b*c*d^2+77*a^3*d^3)*_
+ atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_
+ (b^(15/4)*d^(13/4))-1/64*(15*b^3*c^3+15*a*b^2*c^2*d+_
+ 21*a^2*b*c*d^2+77*a^3*d^3)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_
+ (c+d*x)^(1/4)))/(b^(15/4)*d^(13/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 231a d - 63a b c d - 45a b c d - 45b c )atanh(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 231a d - 63a b c d - 45a b c d - 45b c )atan(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2
+--R (64b d x + (- 88a b d - 72b c d)x + 154a d + 108a b c d + 90b c )
+--R *
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 3 4+-+3 4+-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=x^2/((a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R 4+-------+3 4+-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=-1/8*(5*b*c+7*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+_
+ 1/2*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/16*(5*b^2*c^2+_
+ 6*a*b*c*d+21*a^2*d^2)*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_
+ (c+d*x)^(1/4)))/(b^(11/4)*d^(9/4))+1/16*(5*b^2*c^2+6*a*b*c*d+_
+ 21*a^2*d^2)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_
+ (b^(11/4)*d^(9/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (21a d + 6a b c d + 5b c )atanh(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (21a d + 6a b c d + 5b c )atan(--------------)
+--R 4+-+4+-------+
+--R \|b \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R (8b d x - 14a d - 10b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 2 4+-+3 4+-+
+--R 16b d \|b \|d
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=x/((a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R x
+--R (1) ---------------------
+--R 4+-------+3 4+-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-1/2*(b*c+3*a*d)*atan(d^(1/4)*_
+ (a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(5/4))-_
+ 1/2*(b*c+3*a*d)*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_
+ (c+d*x)^(1/4)))/(b^(7/4)*d^(5/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|d \|b x + a \|d \|b x + a
+--R (- 3a d - b c)atanh(--------------) + (- 3a d - b c)atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|b \|d x + c \|b \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R 2\|b \|d \|b x + a \|d x + c
+--R /
+--R 4+-+3 4+-+
+--R 2b d \|b \|d
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 500
+--m0:=a0-r0
+--E 439
+
+--S 440 of 500
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=1/((a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 4+-------+3 4+-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=2*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/_
+ (b^(3/4)*d^(1/4))+2*atanh(d^(1/4)*(a+b*x)^(1/4)/_
+ (b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(1/4))
+--R
+--R
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|d \|b x + a \|d \|b x + a
+--R 2atanh(--------------) + 2atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|b \|d x + c \|b \|d x + c
+--R (2) ----------------------------------------------
+--R 4+-+3 4+-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 500
+--m0:=a0-r0
+--E 444
+
+--S 445 of 500
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=1/(x*(a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 4+-------+3 4+-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=-2*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(3/4)*c^(1/4))-2*atanh(c^(1/4)*(a+b*x)^(1/4)/_
+ (a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(1/4))
+--R
+--R
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|c \|b x + a \|c \|b x + a
+--R - 2atanh(--------------) - 2atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|a \|d x + c \|a \|d x + c
+--R (2) ------------------------------------------------
+--R 4+-+3 4+-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 500
+--m0:=a0-r0
+--E 449
+
+--S 450 of 500
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=1/(x^2*(a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 2 4+-------+3 4+-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x)+1/2*(3*b*c+a*d)*_
+ atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(5/4))+_
+ 1/2*(3*b*c+a*d)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(7/4)*c^(5/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|c \|b x + a \|c \|b x + a
+--R (a d + 3b c)x atanh(--------------) + (a d + 3b c)x atan(--------------)
+--R 4+-+4+-------+ 4+-+4+-------+
+--R \|a \|d x + c \|a \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R - 2\|a \|c \|b x + a \|d x + c
+--R /
+--R 4+-+3 4+-+
+--R 2a c x \|a \|c
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+--a0:=integrate(t0,x)
+--E 453
+
+--S 454 of 500
+--m0:=a0-r0
+--E 454
+
+--S 455 of 500
+--d0:=D(m0,x)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=1/(x^3*(a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 3 4+-------+3 4+-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^2)+1/8*(7*b*c+5*a*d)*_
+ (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x)-1/16*(21*b^2*c^2+_
+ 6*a*b*c*d+5*a^2*d^2)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*_
+ (c+d*x)^(1/4)))/(a^(11/4)*c^(9/4))-1/16*(21*b^2*c^2+6*a*b*c*d+_
+ 5*a^2*d^2)*atanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(11/4)*c^(9/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 5a d - 6a b c d - 21b c )x atanh(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 5a d - 6a b c d - 21b c )x atan(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R ((10a d + 14b c)x - 8a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 2 4+-+3 4+-+
+--R 16a c x \|a \|c
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 500
+--m0:=a0-r0
+--E 459
+
+--S 460 of 500
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=1/(x^4*(a+b*x)^(3/4)*(c+d*x)^(1/4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 4 4+-------+3 4+-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^3)+1/24*(11*b*c+9*a*d)*_
+ (a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x^2)-_
+ 1/96*(77*b^2*c^2+54*a*b*c*d+45*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/_
+ (a^3*c^3*x)+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+15*a^2*b*c*d^2+_
+ 15*a^3*d^3)*atan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/_
+ (a^(15/4)*c^(13/4))+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+_
+ 15*a^2*b*c*d^2+15*a^3*d^3)*atanh(c^(1/4)*(a+b*x)^(1/4)/_
+ (a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(13/4))
+--R
+--R
+--R (2)
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (45a d + 45a b c d + 63a b c d + 231b c )x atanh(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 4+-+4+-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (45a d + 45a b c d + 63a b c d + 231b c )x atan(--------------)
+--R 4+-+4+-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2
+--R ((- 90a d - 108a b c d - 154b c )x + (72a c d + 88a b c )x - 64a c )
+--R *
+--R 4+-+3 4+-+4+-------+4+-------+3
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 3 3 4+-+3 4+-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 500
+--m0:=a0-r0
+--E 464
+
+--S 465 of 500
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=1/((1-a*x)^(1/4)*(1+b*x)^(3/4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 4+---------+4+-------+3
+--R \|- a x + 1 \|b x + 1
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=-log(-a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+sqrt(a)+_
+ sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*sqrt(2))+_
+ log(a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+_
+ sqrt(a)+sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*_
+ sqrt(2))+atan(1-b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*_
+ (1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4))-atan(1+b^(1/4)*_
+ (1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*(1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4))
+--R
+--R
+--R (2)
+--R log
+--R +-+ +-------+ +---------+ +-+ 4+-------+
+--R (\|a \|b x + 1 + \|- a x + 1 \|b )\|b x + 1
+--R +
+--R +-+4+---------+4+-+4+-+ +-------+
+--R \|2 \|- a x + 1 \|a \|b \|b x + 1
+--R /
+--R +-------+4+-------+
+--R \|b x + 1 \|b x + 1
+--R +
+--R -
+--R log
+--R +-+ +-------+ +---------+ +-+ 4+-------+
+--R (\|a \|b x + 1 + \|- a x + 1 \|b )\|b x + 1
+--R +
+--R +-+4+---------+4+-+4+-+ +-------+
+--R - \|2 \|- a x + 1 \|a \|b \|b x + 1
+--R /
+--R +-------+4+-------+
+--R \|b x + 1 \|b x + 1
+--R +
+--R 4+-+4+-------+ +-+4+---------+4+-+
+--R \|a \|b x + 1 + \|2 \|- a x + 1 \|b
+--R - 2atan(-------------------------------------)
+--R 4+-+4+-------+
+--R \|a \|b x + 1
+--R +
+--R 4+-+4+-------+ +-+4+---------+4+-+
+--R \|a \|b x + 1 - \|2 \|- a x + 1 \|b
+--R 2atan(-------------------------------------)
+--R 4+-+4+-------+
+--R \|a \|b x + 1
+--R /
+--R +-+4+-+4+-+3
+--R \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=1/((1-a*x)^(1/4)*(1+a*x)^(3/4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 4+---------+4+-------+3
+--R \|- a x + 1 \|a x + 1
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=-log(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/sqrt(1+a*x))/_
+ (a*sqrt(2))+log(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/_
+ sqrt(1+a*x))/(a*sqrt(2))+atan(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*_
+ sqrt(2)/a-atan(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*sqrt(2)/a
+--R
+--R
+--R (2)
+--R +-------+ +---------+ 4+-------+ +-+4+---------+ +-------+
+--R (\|a x + 1 + \|- a x + 1 )\|a x + 1 + \|2 \|- a x + 1 \|a x + 1
+--R log(------------------------------------------------------------------)
+--R +-------+4+-------+
+--R \|a x + 1 \|a x + 1
+--R +
+--R +-------+ +---------+ 4+-------+ +-+4+---------+ +-------+
+--R (\|a x + 1 + \|- a x + 1 )\|a x + 1 - \|2 \|- a x + 1 \|a x + 1
+--R - log(------------------------------------------------------------------)
+--R +-------+4+-------+
+--R \|a x + 1 \|a x + 1
+--R +
+--R 4+-------+ +-+4+---------+
+--R \|a x + 1 + \|2 \|- a x + 1
+--R - 2atan(-----------------------------)
+--R 4+-------+
+--R \|a x + 1
+--R +
+--R 4+-------+ +-+4+---------+
+--R \|a x + 1 - \|2 \|- a x + 1
+--R 2atan(-----------------------------)
+--R 4+-------+
+--R \|a x + 1
+--R /
+--R +-+
+--R a\|2
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-%i*x)^(1/6*%i)*x^3/(1+%i*x)^(1/6*%i)
+--R
+--R
+--R %i
+--R --
+--R 3 6
+--R x (- %i x + 1)
+--R (1) ----------------
+--R %i
+--R --
+--R 6
+--R (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 476
+
+--S 477 of 500
+--r0:=1/4*x^4*AppellF1(4,-1/6*%i,1/6*%i,5,%i*x,-%i*x),(-18/37+3/37*%i)*_
+-- 2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*AppellF1(1+1/6*%i,1/6*%i,_
+-- -3,2+1/6*%i,1/2*(1-%i*x),1-%i*x)
+--E 477
+
+--S 478 of 500
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-%i*x)^(1/6*%i)*x^2/(1+%i*x)^(1/6*%i)
+--R
+--R
+--R %i
+--R --
+--R 2 6
+--R x (- %i x + 1)
+--R (1) ----------------
+--R %i
+--R --
+--R 6
+--R (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 481
+
+--S 482 of 500
+--r0:=-1/18*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)+_
+-- 1/3*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)*x+_
+-- (-17/333+34/111*%i)*2^(1/6*%i)*(1+%i*x)^(1-1/6*%i)*_
+-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x))
+--E 482
+
+--S 483 of 500
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 500
+--m0:=a0-r0
+--E 484
+
+--S 485 of 500
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-%i*x)^(1/6*%i)*x/(1+%i*x)^(1/6*%i)
+--R
+--R
+--R %i
+--R --
+--R 6
+--R x (- %i x + 1)
+--R (1) ----------------
+--R %i
+--R --
+--R 6
+--R (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 486
+
+--S 487 of 500
+--r0:=1/2*(1-%i*x)^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)+_
+-- (-1/37+6/37*%i)*2^(1/6*%i)*(1+%i*x)^(1-1/6*%i)*_
+-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x))
+--E 487
+
+--S 488 of 500
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 500
+--m0:=a0-r0
+--E 489
+
+--S 490 of 500
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-%i*x)^(1/6*%i)/(1+%i*x)^(1/6*%i)
+--R
+--R
+--R %i
+--R --
+--R 6
+--R (- %i x + 1)
+--R (1) --------------
+--R %i
+--R --
+--R 6
+--R (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 491
+
+--S 492 of 500
+--r0:=(3/37-18/37*%i)*2^(1+1/6*%i)*(1+%i*x)^(1-1/6*%i)*_
+-- hypergeometric(-1/6*%i,1-1/6*%i,2-1/6*%i,1/2*(1+%i*x))
+--E 492
+
+--S 493 of 500
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 500
+--m0:=a0-r0
+--E 494
+
+--S 495 of 500
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x)
+--R
+--R
+--R %i
+--R --
+--R 6
+--R (- %i x + 1)
+--R (1) --------------
+--R %i
+--R --
+--R 6
+--R x (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 496
+
+--S 497 of 500
+--r0:-(-18/37+3/37*%i)*2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*
+-- AppellF1(1+1/6*%i,1/6*%i,1,2+1/6*%i,1/2*(1-%i*x),1-%i*x)
+--E 497
+
+--S 498 of 500
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 500
+--m0:=a0-r0
+--E 499
+
+--S 500 of 500
+--d0:=D(m0,x)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
+
diff --git a/src/axiom-website/CATS/rich3c.input.pdf b/src/axiom-website/CATS/rich3c.input.pdf
new file mode 100644
index 0000000..5182c84
Binary files /dev/null and b/src/axiom-website/CATS/rich3c.input.pdf differ
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index e5fec42..5cd6db4 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -4250,6 +4250,8 @@ src/axiom-website/CATS/rich1b statistics update
src/axiom-website/CATS/rich2, rich3a
20130726.01.tpd.patch
src/axiom-website/CATS/rich3b
+20130727.01.tpd.patch
+src/axiom-website/CATS/rich3c