diff --git a/changelog b/changelog
index 7ac15d0..9fd4a40 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,9 @@
+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
+20130726 tpd src/axiom-website/CATS/rich3b.input.pdf added
+20130726 tpd src/input/Makefile add rich3b
+20130726 tpd src/input/rich3b.input added
20130725 tpd src/axiom-website/patches.html 20130725.01.tpd.patch
20130725 tpd src/axiom-website/CATS/index.html add rich2, rich3a
20130725 tpd src/axiom-website/CATS/rich2.input added
diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html
index e975cda..ad1f519 100644
--- a/src/axiom-website/CATS/index.html
+++ b/src/axiom-website/CATS/index.html
@@ -299,6 +299,9 @@ They have been rewritten using Axiom syntax.
(a+b x)^m (c+d)^n (e+f x)^p (part 1)
source
pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 2)
+ source
+ pdf
Rich
diff --git a/src/axiom-website/CATS/rich3b.input.pamphlet b/src/axiom-website/CATS/rich3b.input.pamphlet
new file mode 100644
index 0000000..efdbbf9
--- /dev/null
+++ b/src/axiom-website/CATS/rich3b.input.pamphlet
@@ -0,0 +1,11568 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3b.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 200 integrals in this file.
+\item 200 supplied "optimal results".
+\item 5 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 195 cases that Axiom failed to integrate.
+\item 0 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3b.output
+)spool rich3b.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1000
+t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^4
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1000
+r0:=2*d^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)-_
+ 1/8*(b^3*c^3-5*a*b^2*c^2*d+15*a^2*b*c*d^2+5*a^3*d^3)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*sqrt(c))-_
+ 1/12*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^2)-1/3*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/x^3+1/8*(b*c-5*a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 3 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 48a d x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 15a d - 45a b c d + 15a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((- 33a d - 14a b c d + 3b c )x + (- 26a c d - 2a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 24a x \|a \|c
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1000
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 1000
+--m0:=a0-r0
+--E 4
+
+--S 5 of 1000
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 1000
+t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^5
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1000
+r0:=5/64*(b*c-a*d)^4*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(7/2)*c^(3/2))+5/96*(b*c-a*d)^2*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(a^2*c*x^2)-1/24*(b*c-a*d)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(a*c*x^3)-1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/(c*x^4)-_
+ 5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d - 60a b c d + 90a b c d - 60a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 15a d - 73a b c d + 55a b c d - 15b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 118a c d - 36a b c d + 10a b c )x + (- 136a c d - 8a b c )x
+--R +
+--R 3 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1000
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 1000
+--m0:=a0-r0
+--E 9
+
+--S 10 of 1000
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 1000
+t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^6
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1000
+r0:=-1/128*(b*c-a*d)^4*(7*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(9/2)*c^(5/2))-1/40*(b*c+5*a*d)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(a*x^4)-1/5*(c+d*x)^(5/2)*sqrt(a+b*x)/x^5+1/240*_
+ (b*c-3*a*d)*(7*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^3)-_
+ 1/960*(35*b^3*c^3-111*a*b^2*c^2*d+109*a^2*b*c*d^2+15*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c*x^2)+1/1920*(105*b^4*c^4-_
+ 340*a*b^3*c^3*d+346*a^2*b^2*c^2*d^2-60*a^3*b*c*d^3+45*a^4*d^4)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^2*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 45a d + 75a b c d + 150a b c d - 450a b c d + 375a b c d
+--R +
+--R 5 5
+--R - 105b c
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (45a d - 60a b c d + 346a b c d - 340a b c d + 105b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (- 30a c d - 218a b c d + 222a b c d - 70a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2 4 3 3 4
+--R (- 744a c d - 176a b c d + 56a b c )x + (- 1008a c d - 48a b c )x
+--R +
+--R 4 4
+--R - 384a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 4 2 5 +-+ +-+
+--R 1920a c x \|a \|c
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1000
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 1000
+--m0:=a0-r0
+--E 14
+
+--S 15 of 1000
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 1000
+t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^7
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1000
+r0:=1/512*(b*c-a*d)^4*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*c^(7/2))-_
+ 1/60*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^5)-_
+ 1/6*(c+d*x)^(5/2)*sqrt(a+b*x)/x^6+1/160*(3*b^2*c^2-6*a*b*c*d-_
+ 5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^4)-1/960*(21*b^3*c^3-_
+ 61*a*b^2*c^2*d+51*a^2*b*c*d^2+5*a^3*d^3)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^3*c*x^3)+1/3840*(105*b^4*c^4-308*a*b^3*c^3*d+_
+ 262*a^2*b^2*c^2*d^2-20*a^3*b*c*d^3+25*a^4*d^4)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^4*c^2*x^2)-1/7680*(315*b^5*c^5-945*a*b^4*c^4*d+_
+ 838*a^2*b^3*c^3*d^2-90*a^3*b^2*c^2*d^3-65*a^4*b*c*d^4+75*a^5*d^5)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^5*c^3*x)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 75a d - 90a b c d - 75a b c d - 300a b c d + 1125a b c d
+--R +
+--R 5 5 6 6
+--R - 1050a b c d + 315b c
+--R *
+--R +-+ +-------+
+--R 6 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 75a d + 65a b c d + 90a b c d - 838a b c d + 945a b c d
+--R +
+--R 5 5
+--R - 315b c
+--R *
+--R 5
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4
+--R (50a c d - 40a b c d + 524a b c d - 616a b c d + 210a b c )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 3
+--R (- 40a c d - 408a b c d + 488a b c d - 168a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5 2
+--R (- 2160a c d - 416a b c d + 144a b c )x
+--R +
+--R 5 4 4 5 5 5
+--R (- 3200a c d - 128a b c )x - 1280a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 5 3 6 +-+ +-+
+--R 7680a c x \|a \|c
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 1000
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 1000
+--m0:=a0-r0
+--E 19
+
+--S 20 of 1000
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 1000
+t0:=x^3*sqrt(a+b*x)/sqrt(c+d*x)
+--R
+--R
+--R 3 +-------+
+--R x \|b x + a
+--R (1) ------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1000
+r0:=1/64*(b*c-a*d)*(35*b^3*c^3+15*a*b^2*c^2*d+9*a^2*b*c*d^2+5*a^3*d^3)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(9/2))-_
+ 1/192*(105*b^3*c^3-25*a*b^2*c^2*d-17*a^2*b*c*d^2-15*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4)-1/96*(6*a*c-35*b*c^2/d+5*a^2*d/b)*_
+ x*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)-1/24*(7*b*c-a*d)*x^2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b*d^2)+1/4*x^3*sqrt(a+b*x)*sqrt(c+d*x)/d
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d - 12a b c d - 18a b c d - 60a b c d + 105b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (8a b d - 56b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2
+--R (- 10a b d - 12a b c d + 70b c d)x + 15a d + 17a b c d
+--R +
+--R 2 2 3 3
+--R 25a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 4 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1000
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 1000
+--m0:=a0-r0
+--E 24
+
+--S 25 of 1000
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 1000
+t0:=x^2*sqrt(a+b*x)/sqrt(c+d*x)
+--R
+--R
+--R 2 +-------+
+--R x \|b x + a
+--R (1) ------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1000
+r0:=-1/8*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))-1/12*(5*b*c+3*a*d)*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^2)+1/3*x*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(b*d)+1/8*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^2*d^3)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (3a d + 3a b c d + 9a b c d - 15b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (2a b d - 10b c d)x - 3a d - 4a b c d + 15b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 24b d \|b \|d
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 1000
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 1000
+--m0:=a0-r0
+--E 29
+
+--S 30 of 1000
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 1000
+t0:=x*sqrt(a+b*x)/sqrt(c+d*x)
+--R
+--R
+--R +-------+
+--R x\|b x + a
+--R (1) -----------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1000
+r0:=1/4*(b*c-a*d)*(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(3/2)*d^(5/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)-_
+ 1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (- a d - 2a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (2b d x + a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4b d \|b \|d
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1000
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 1000
+--m0:=a0-r0
+--E 34
+
+--S 35 of 1000
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 1000
+t0:=sqrt(a+b*x)/sqrt(c+d*x)
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ----------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1000
+r0:=-(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (d^(3/2)*sqrt(b))+sqrt(a+b*x)*sqrt(c+d*x)/d
+--R
+--R
+--R +-+ +-------+
+--R \|d \|b x + a +-+ +-+ +-------+ +-------+
+--R (a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|b \|d x + c
+--R (2) ---------------------------------------------------------------
+--R +-+ +-+
+--R d\|b \|d
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1000
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 1000
+--m0:=a0-r0
+--E 39
+
+--S 40 of 1000
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 1000
+t0:=sqrt(a+b*x)/(x*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) -----------
+--R +-------+
+--R x\|d x + c
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/sqrt(c)+_
+ 2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/sqrt(d)
+--R
+--R
+--R +-+ +-------+ +-+ +-------+
+--R +-+ +-+ \|d \|b x + a +-+ +-+ \|c \|b x + a
+--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------)
+--R +-+ +-------+ +-+ +-------+
+--R \|b \|d x + c \|a \|d x + c
+--R (2) ---------------------------------------------------------------
+--R +-+ +-+
+--R \|c \|d
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1000
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 1000
+--m0:=a0-r0
+--E 44
+
+--S 45 of 1000
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 1000
+t0:=sqrt(a+b*x)/(x^2*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ------------
+--R 2 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1000
+r0:=-(b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*_
+ sqrt(a))-sqrt(a+b*x)*sqrt(c+d*x)/(c*x)
+--R
+--R
+--R +-+ +-------+
+--R \|c \|b x + a +-+ +-+ +-------+ +-------+
+--R (a d - b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|a \|d x + c
+--R (2) -----------------------------------------------------------------
+--R +-+ +-+
+--R c x\|a \|c
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 1000
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 1000
+--m0:=a0-r0
+--E 49
+
+--S 50 of 1000
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 1000
+t0:=sqrt(a+b*x)/(x^3*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ------------
+--R 3 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1000
+r0:=1/4*(b*c-a*d)*(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(3/2)*c^(5/2))-1/2*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^2)-_
+ 1/4*(b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 3a d + 2a b c d + b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R ((3a d - b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4a c x \|a \|c
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 1000
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 1000
+--m0:=a0-r0
+--E 54
+
+--S 55 of 1000
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 1000
+t0:=sqrt(a+b*x)/(x^4*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ------------
+--R 4 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1000
+r0:=-1/8*(b*c-a*d)*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/_
+ (c*x^3)-1/12*(b*c-5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x^2)+_
+ 1/24*(3*b*c-5*a*d)*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (15a d - 9a b c d - 3a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((- 15a d + 4a b c d + 3b c )x + (10a c d - 2a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 2 3 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 1000
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 1000
+--m0:=a0-r0
+--E 59
+
+--S 60 of 1000
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 1000
+t0:=sqrt(a+b*x)/(x^5*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ------------
+--R 5 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1000
+r0:=1/64*(b*c-a*d)*(5*b^3*c^3+9*a*b^2*c^2*d+15*a^2*b*c*d^2+35*a^3*d^3)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))-_
+ 1/4*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^4)-1/24*(b*c-7*a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a*c^2*x^3)+1/96*(5*b^2*c^2+6*a*b*c*d-35*a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x^2)-1/192*(15*b^3*c^3+17*a*b^2*c^2*d+_
+ 25*a^2*b*c*d^2-105*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^4*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 105a d + 60a b c d + 18a b c d + 12a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (105a d - 25a b c d - 17a b c d - 15b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (- 70a c d + 12a b c d + 10a b c )x + (56a c d - 8a b c )x - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 4 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 1000
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 1000
+--m0:=a0-r0
+--E 64
+
+--S 65 of 1000
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 1000
+t0:=x^2*sqrt(a+b*x)/(c+d*x)^(3/2)
+--R
+--R
+--R 2 +-------+
+--R x \|b x + a
+--R (1) -------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1000
+r0:=1/4*(15*b^2*c^2-6*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(3/2)*d^(7/2))+2*c^2*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*_
+ sqrt(c+d*x))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^2)+1/4*(6*a*c-_
+ 15*b*c^2/d+a^2*d/b)*sqrt(a+b*x)*sqrt(c+d*x)/(d^2*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ \|d \|b x + a
+--R (- a d - 6a b c d + 15b c )\|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+
+--R (2b d x + (a d - 5b c d)x + a c d - 15b c )\|b \|d \|b x + a
+--R /
+--R 3 +-+ +-+ +-------+
+--R 4b d \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 1000
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 1000
+--m0:=a0-r0
+--E 69
+
+--S 70 of 1000
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 1000
+t0:=x*sqrt(a+b*x)/(c+d*x)^(3/2)
+--R
+--R
+--R +-------+
+--R x\|b x + a
+--R (1) -------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1000
+r0:=-(3*b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (d^(5/2)*sqrt(b))-2*c*(a+b*x)^(3/2)/(d*(b*c-a*d)*sqrt(c+d*x))+_
+ (3*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(d^2*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a +-+ +-+ +-------+
+--R (a d - 3b c)\|d x + c atanh(--------------) + (d x + 3c)\|b \|d \|b x + a
+--R +-+ +-------+
+--R \|b \|d x + c
+--R --------------------------------------------------------------------------
+--R 2 +-+ +-+ +-------+
+--R d \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 1000
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 1000
+--m0:=a0-r0
+--E 74
+
+--S 75 of 1000
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 1000
+t0:=sqrt(a+b*x)/(c+d*x)^(3/2)
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) -------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1000
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(3/2)-_
+ 2*sqrt(a+b*x)/(d*sqrt(c+d*x))
+--R
+--R
+--R +-+ +-------+
+--R +-+ +-------+ \|d \|b x + a +-+ +-------+
+--R 2\|b \|d x + c atanh(--------------) - 2\|d \|b x + a
+--R +-+ +-------+
+--R \|b \|d x + c
+--R (2) ------------------------------------------------------
+--R +-+ +-------+
+--R d\|d \|d x + c
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 1000
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 1000
+--m0:=a0-r0
+--E 79
+
+--S 80 of 1000
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 1000
+t0:=sqrt(a+b*x)/(x*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ----------------------
+--R 2 +-------+
+--R (d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(3/2)+_
+ 2*sqrt(a+b*x)/(c*sqrt(c+d*x))
+--R
+--R
+--R +-+ +-------+
+--R +-+ +-------+ \|c \|b x + a +-+ +-------+
+--R - 2\|a \|d x + c atanh(--------------) + 2\|c \|b x + a
+--R +-+ +-------+
+--R \|a \|d x + c
+--R (2) --------------------------------------------------------
+--R +-+ +-------+
+--R c\|c \|d x + c
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 1000
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 1000
+--m0:=a0-r0
+--E 84
+
+--S 85 of 1000
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 1000
+t0:=sqrt(a+b*x)/(x^2*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) -----------------------
+--R 3 2 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1000
+r0:=-(b*c-3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*_
+ sqrt(a))-3*d*sqrt(a+b*x)/(c^2*sqrt(c+d*x))-sqrt(a+b*x)/(c*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a +-+ +-+ +-------+
+--R (3a d - b c)x\|d x + c atanh(--------------) + (- 3d x - c)\|a \|c \|b x + a
+--R +-+ +-------+
+--R \|a \|d x + c
+--R -----------------------------------------------------------------------------
+--R 2 +-+ +-+ +-------+
+--R c x\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 1000
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 1000
+--m0:=a0-r0
+--E 89
+
+--S 90 of 1000
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 1000
+t0:=sqrt(a+b*x)/(x^3*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) -----------------------
+--R 4 3 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1000
+r0:=1/4*(b^2*c^2+6*a*b*c*d-15*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(3/2)*c^(7/2))-1/4*d*(b*c-15*a*d)*sqrt(a+b*x)/_
+ (a*c^3*sqrt(c+d*x))-1/2*sqrt(a+b*x)/(c*x^2*sqrt(c+d*x))-_
+ 1/4*(b*c-5*a*d)*sqrt(a+b*x)/(a*c^2*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-------+ \|c \|b x + a
+--R (- 15a d + 6a b c d + b c )x \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+
+--R ((15a d - b c d)x + (5a c d - b c )x - 2a c )\|a \|c \|b x + a
+--R /
+--R 3 2 +-+ +-+ +-------+
+--R 4a c x \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 1000
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 1000
+--m0:=a0-r0
+--E 94
+
+--S 95 of 1000
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 1000
+t0:=x^3*sqrt(a+b*x)/(c+d*x)^(5/2)
+--R
+--R
+--R 3 +-------+
+--R x \|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1000
+r0:=1/4*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(9/2))-2/3*x^3*sqrt(a+b*x)/_
+ (d*(c+d*x)^(3/2))-2/3*(7*b*c-6*a*d)*x^2*sqrt(a+b*x)/(d^2*(b*c-a*d)*_
+ sqrt(c+d*x))-1/12*(105*b^2*c^2-100*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b*d^4*(b*c-a*d))+1/6*(35*b*c-31*a*d)*x*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(d^3*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 3 3
+--R (- 3a d - 27a b c d + 135a b c d - 105b c d)x - 3a c d
+--R +
+--R 2 2 2 2 3 3 4
+--R - 27a b c d + 135a b c d - 105b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 2 3 3 2 4 3 2 2 2 2
+--R (6a b d - 6b c d )x + (3a d - 24a b c d + 21b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 3 2 4
+--R (6a c d - 138a b c d + 140b c d)x + 3a c d - 100a b c d + 105b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 6 2 5 5 2 2 4 +-+ +-+ +-------+
+--R ((12a b d - 12b c d )x + 12a b c d - 12b c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 1000
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 1000
+--m0:=a0-r0
+--E 99
+
+--S 100 of 1000
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 1000
+t0:=x^2*sqrt(a+b*x)/(c+d*x)^(5/2)
+--R
+--R
+--R 2 +-------+
+--R x \|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1000
+r0:=2/3*c^2*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))-(5*b*c-a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(7/2)*sqrt(b))-_
+ 4*c*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+(5*b*c-a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(d^3*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 3
+--R ((3a d - 18a b c d + 15b c d)x + 3a c d - 18a b c d + 15b c )
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 2 2 2 2 2 3 +-+
+--R ((3a d - 3b c d )x + (18a c d - 20b c d)x + 13a c d - 15b c )\|b
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R /
+--R 5 4 4 2 3 +-+ +-+ +-------+
+--R ((3a d - 3b c d )x + 3a c d - 3b c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 1000
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 1000
+--m0:=a0-r0
+--E 104
+
+--S 105 of 1000
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 1000
+t0:=x*sqrt(a+b*x)/(c+d*x)^(5/2)
+--R
+--R
+--R +-------+
+--R x\|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1000
+r0:=-2/3*c*(a+b*x)^(3/2)/(d*(b*c-a*d)*(c+d*x)^(3/2))+2*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(5/2)-2*sqrt(a+b*x)/_
+ (d^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-------+ \|d \|b x + a
+--R ((6a d - 6b c d)x + 6a c d - 6b c )\|b \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 +-+ +-------+
+--R ((- 6a d + 8b c d)x - 4a c d + 6b c )\|d \|b x + a
+--R /
+--R 4 3 3 2 2 +-+ +-------+
+--R ((3a d - 3b c d )x + 3a c d - 3b c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 1000
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 1000
+--m0:=a0-r0
+--E 109
+
+--S 110 of 1000
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 1000
+t0:=sqrt(a+b*x)/(c+d*x)^(5/2)
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1000
+r0:=2/3*(a+b*x)^(3/2)/((b*c-a*d)*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (- 2b x - 2a)\|b x + a
+--R (2) ----------------------------------------------
+--R 2 2 +-------+
+--R ((3a d - 3b c d)x + 3a c d - 3b c )\|d x + c
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 1000 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 +-------+ +-------+ 2 2 2
+--R (- 8b c x - 8a c )\|b x + a \|d x + c + (a c + 16a )d x
+--R +
+--R 2 2 3 2 2
+--R (2a c + 32a c)d x + a c + 16a c
+--R /
+--R 2 3 3 2 2 3 2 4 4 5
+--R (12a c d - 12b c d )x + (24a c d - 24b c d)x + 12a c d - 12b c
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 1000 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2
+--R a c + 16a
+--R (4) ----------------
+--R 2 3
+--R 12a c d - 12b c
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1000
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 1000
+t0:=sqrt(a+b*x)/(x*(c+d*x)^(5/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) --------------------------------
+--R 2 3 2 2 +-------+
+--R (d x + 2c d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(5/2)+_
+ 2/3*sqrt(a+b*x)/(c*(c+d*x)^(3/2))+2/3*(2*b*c-3*a*d)*sqrt(a+b*x)/_
+ (c^2*(b*c-a*d)*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-------+ \|c \|b x + a
+--R ((- 6a d + 6b c d)x - 6a c d + 6b c )\|a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-------+
+--R ((6a d - 4b c d)x + 8a c d - 6b c )\|c \|b x + a
+--R /
+--R 2 2 3 3 4 +-+ +-------+
+--R ((3a c d - 3b c d)x + 3a c d - 3b c )\|c \|d x + c
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 1000
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 1000
+--m0:=a0-r0
+--E 119
+
+--S 120 of 1000
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 1000
+t0:=sqrt(a+b*x)/(x^2*(c+d*x)^(5/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ---------------------------------
+--R 2 4 3 2 2 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1000
+r0:=-(b*c-5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (c^(7/2)*sqrt(a))-5/3*d*sqrt(a+b*x)/(c^2*(c+d*x)^(3/2))-sqrt(a+b*x)/_
+ (c*x*(c+d*x)^(3/2))-1/3*d*(13*b*c-15*a*d)*sqrt(a+b*x)/_
+ (c^3*(b*c-a*d)*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((15a d - 18a b c d + 3b c d)x + (15a c d - 18a b c d + 3b c )x)
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 2 2 2 2 2 3
+--R ((- 15a d + 13b c d )x + (- 20a c d + 18b c d)x - 3a c d + 3b c )
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 3 2 4 2 4 5 +-+ +-+ +-------+
+--R ((3a c d - 3b c d)x + (3a c d - 3b c )x)\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1000
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 1000
+--m0:=a0-r0
+--E 124
+
+--S 125 of 1000
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 1000
+t0:=sqrt(a+b*x)/(x^3*(c+d*x)^(5/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) ---------------------------------
+--R 2 5 4 2 3 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1000
+r0:=1/4*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(9/2))-1/12*d*(3*b*c-35*a*d)*_
+ sqrt(a+b*x)/(a*c^3*(c+d*x)^(3/2))-1/2*sqrt(a+b*x)/(c*x^2*(c+d*x)^(3/2))-_
+ 1/4*(b*c-7*a*d)*sqrt(a+b*x)/(a*c^2*x*(c+d*x)^(3/2))-_
+ 1/12*d*(3*b^2*c^2-100*a*b*c*d+105*a^2*d^2)*sqrt(a+b*x)/_
+ (a*c^4*(b*c-a*d)*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 3
+--R (- 105a d + 135a b c d - 27a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (- 105a c d + 135a b c d - 27a b c d - 3b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 4 3 2 2 2 3
+--R (105a d - 100a b c d + 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2
+--R (140a c d - 138a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4 2 3 4
+--R (21a c d - 24a b c d + 3b c )x - 6a c d + 6a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 2 4 2 5 3 2 5 6 2 +-+ +-+ +-------+
+--R ((12a c d - 12a b c d)x + (12a c d - 12a b c )x )\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 1000
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 1000
+--m0:=a0-r0
+--E 129
+
+--S 130 of 1000
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 1000
+t0:=x^2*(a+b*x)^(3/2)*sqrt(c+d*x)
+--R
+--R
+--R 3 2 +-------+ +-------+
+--R (1) (b x + a x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1000
+r0:=-1/40*(7*b*c+5*a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^2*d^2)+_
+ 1/5*x*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b*d)+1/128*(b*c-a*d)^3*_
+ (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))+1/192*(b*c-a*d)*_
+ (7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (b^3*d^3)+1/48*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b^3*d^2)-1/128*(b*c-a*d)^2*(7*b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--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
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 384b d x + (528a b d + 48b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (24a b d + 96a b c d - 56b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (- 30a b d + 18a b c d - 122a b c d + 70b c d)x + 45a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 30a b c d - 36a b c d + 190a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 4 +-+ +-+
+--R 1920b d \|b \|d
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 1000
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 1000
+--m0:=a0-r0
+--E 134
+
+--S 135 of 1000
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 1000
+t0:=x*(a+b*x)^(3/2)*sqrt(c+d*x)
+--R
+--R
+--R 2 +-------+ +-------+
+--R (1) (b x + a x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1000
+r0:=1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b*d)-1/64*(b*c-a*d)^3*(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))-_
+ 1/96*(b*c-a*d)*(5*b*c+3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^2)-_
+ 1/24*(5*b*c+3*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d)+1/64*(b*c-a*d)^2*_
+ (5*b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (9a d - 12a b c d - 18a b c d + 36a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2
+--R 48b d x + (72a b d + 8b c d )x + (6a b d + 20a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R - 9a d + 9a b c d - 31a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 1000
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 1000
+--m0:=a0-r0
+--E 139
+
+--S 140 of 1000
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)
+--R
+--R
+--R +-------+ +-------+
+--R (1) (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1000
+r0:=1/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(3/2)*d^(5/2))+1/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)+_
+ 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/b-1/8*(b*c-a*d)^2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b*d^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 3a d + 9a b c d - 9a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (14a b d + 2b c d)x + 3a d + 8a b c d - 3b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 24b d \|b \|d
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 1000
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 1000
+--m0:=a0-r0
+--E 144
+
+--S 145 of 1000
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)/x
+--R
+--R
+--R +-------+ +-------+
+--R (b x + a)\|b x + a \|d x + c
+--R (1) -----------------------------
+--R x
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1000
+r0:=-1/4*(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)))/(d^(3/2)*sqrt(b))-2*a^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))*sqrt(c)+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)+_
+ 1/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d + 6a b c d - b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ +-+ +-+ \|c \|b x + a
+--R - 8a d\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (2b d x + 5a d + b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 4d\|b \|d
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 1000
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 1000
+--m0:=a0-r0
+--E 149
+
+--S 150 of 1000
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)/x^2
+--R
+--R
+--R +-------+ +-------+
+--R (b x + a)\|b x + a \|d x + c
+--R (1) -----------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1000
+r0:=-(3*b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/_
+ sqrt(c)+(b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(b)/sqrt(d)-(a+b*x)^(3/2)*sqrt(c+d*x)/x+2*b*sqrt(a+b*x)*sqrt(c+d*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ \|d \|b x + a
+--R (3a d + b c)x\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ \|c \|b x + a
+--R (- a d - 3b c)x\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (b x - a)\|c \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R x\|c \|d
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1000
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 1000
+--m0:=a0-r0
+--E 154
+
+--S 155 of 1000
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)/x^3
+--R
+--R
+--R +-------+ +-------+
+--R (b x + a)\|b x + a \|d x + c
+--R (1) -----------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1000
+r0:=-1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*sqrt(a))+2*b^(3/2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)-1/2*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/x^2-1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 8b c x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (a d - 6a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R ((- a d - 5b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4c x \|a \|c
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 1000
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 1000
+--m0:=a0-r0
+--E 159
+
+--S 160 of 1000
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)/x^4
+--R
+--R
+--R +-------+ +-------+
+--R (b x + a)\|b x + a \|d x + c
+--R (1) -----------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 1000
+r0:=-1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x^3)+1/8*(b*c-a*d)^3*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))-_
+ 1/4*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c^2*x^2)-1/8*(b*c-a*d)^2*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 3a d + 9a b c d - 9a b c d + 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R ((3a d - 8a b c d - 3b c )x + (- 2a c d - 14a b c )x - 8a c )\|a \|c
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 1000
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 1000
+--m0:=a0-r0
+--E 164
+
+--S 165 of 1000
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)/x^5
+--R
+--R
+--R +-------+ +-------+
+--R (b x + a)\|b x + a \|d x + c
+--R (1) -----------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1000
+r0:=-1/64*(b*c-a*d)^3*(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))-1/4*(a+b*x)^(3/2)*sqrt(c+d*x)/x^4-_
+ 1/24*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^3)-1/96*(3*b^2*c/a+_
+ 10*b*d-5*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^2)+1/192*(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)*_
+ sqrt(c+d*x)/(a^2*c^3*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 15a d + 31a b c d - 9a b c d + 9b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (10a c d - 20a b c d - 6a b c )x + (- 8a c d - 72a b c )x - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 3 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 1000
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 1000
+--m0:=a0-r0
+--E 169
+
+--S 170 of 1000
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 1000
+t0:=(a+b*x)^(3/2)*sqrt(c+d*x)/x^6
+--R
+--R
+--R +-------+ +-------+
+--R (b x + a)\|b x + a \|d x + c
+--R (1) -----------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 1000
+r0:=1/128*(b*c-a*d)^3*(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))-_
+ 1/5*(a+b*x)^(3/2)*sqrt(c+d*x)/x^5-1/40*(3*b*c+a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(c*x^4)-1/240*(3*b^2*c/a+12*b*d-7*a*d^2/c)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(c*x^3)+1/960*(15*b^3*c^3-9*a*b^2*c^2*d+61*a^2*b*c*d^2-_
+ 35*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x^2)-1/1920*(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)*sqrt(c+d*x)/(a^3*c^4*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--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
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (105a d - 190a b c d + 36a b c d + 30a b c d - 45b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (- 70a c d + 122a b c d - 18a b c d + 30a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2 4 3 3 4
+--R (56a c d - 96a b c d - 24a b c )x + (- 48a c d - 528a b c )x
+--R +
+--R 4 4
+--R - 384a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 4 5 +-+ +-+
+--R 1920a c x \|a \|c
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 1000
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 1000
+--m0:=a0-r0
+--E 174
+
+--S 175 of 1000
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 1000
+t0:=x^2*(a+b*x)^(3/2)*(c+d*x)^(3/2)
+--R
+--R
+--R 4 3 2 +-------+ +-------+
+--R (1) (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1000
+r0:=-1/96*(4*a*b*c*d-7*(b*c+a*d)^2)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^3*d^2)-_
+ 7/60*(b*c+a*d)*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b^2*d^2)+1/6*x*_
+ (a+b*x)^(5/2)*(c+d*x)^(5/2)/(b*d)-1/512*(b*c-a*d)^4*(4*a*b*c*d-7*_
+ (b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(9/2)*d^(9/2))-1/768*(b*c-a*d)^2*(4*a*b*c*d-7*(b*c+a*d)^2)*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^3)-1/192*(b*c-a*d)*(4*a*b*c*d-_
+ 7*(b*c+a*d)^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^4*d^2)+1/512*(b*c-a*d)^3*_
+ (4*a*b*c*d-7*(b*c+a*d)^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 105a d - 270a b c d + 135a b c d + 60a b c d + 135a b c d
+--R +
+--R 5 5 6 6
+--R - 270a b c d + 105b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 5 5 4 5 5 4 4
+--R 1280b d x + (1664a b d + 1664b c d )x
+--R +
+--R 2 3 5 4 4 5 2 3 3
+--R (48a b d + 2336a b c d + 48b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5 3 2 2
+--R (- 56a b d + 120a b c d + 120a b c d - 56b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4
+--R (70a b d - 152a b c d + 36a b c d - 152a b c d + 70b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 105a d + 235a b c d - 66a b c d - 66a b c d + 235a b c d
+--R +
+--R 5 5
+--R - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 4 +-+ +-+
+--R 7680b d \|b \|d
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 1000
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 1000
+--m0:=a0-r0
+--E 179
+
+--S 180 of 1000
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 1000
+t0:=x*(a+b*x)^(3/2)*(c+d*x)^(3/2)
+--R
+--R
+--R 3 2 +-------+ +-------+
+--R (1) (b d x + (a d + b c)x + a c x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 1000
+r0:=-1/8*(b*c+a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^2*d)+1/5*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)/(b*d)-3/128*(b*c-a*d)^4*(b*c+a*d)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-1/64*_
+ (b*c-a*d)^2*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)-_
+ 1/16*(b*c-a*d)*(b*c+a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d)+_
+ 3/128*(b*c-a*d)^3*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 15a d + 45a b c d - 30a b c d - 30a b c d + 45a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 128b d x + (176a b d + 176b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (8a b d + 272a b c d + 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (- 10a b d + 26a b c d + 26a b c d - 10b c d)x + 15a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 40a b c d + 18a b c d - 40a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 640b d \|b \|d
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1000
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 1000
+--m0:=a0-r0
+--E 184
+
+--S 185 of 1000
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)
+--R
+--R
+--R 2 +-------+ +-------+
+--R (1) (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 1000
+r0:=1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/b+3/64*(b*c-a*d)^4*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))+1/32*_
+ (b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*(b*c-a*d)*_
+ (a+b*x)^(5/2)*sqrt(c+d*x)/b^2-3/64*(b*c-a*d)^3*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^2*d^2)
+--R
+--R
+--R (2)
+--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 *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2
+--R 16b d x + (24a b d + 24b c d )x + (2a b d + 44a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R - 3a d + 11a b c d + 11a b c d - 3b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 64b d \|b \|d
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1000
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 1000
+--m0:=a0-r0
+--E 189
+
+--S 190 of 1000
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)/x
+--R
+--R
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R (1) -------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1000
+r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)-2*a^(3/2)*c^(3/2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))-1/8*(b*c+a*d)*(b^2*c^2-_
+ 10*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(3/2)*d^(3/2))+1/4*(b*c+a*d)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/d+1/8*(8*a*c-b*c^2/d+a^2*d/b)*sqrt(a+b*x)*sqrt(c+d*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 3a d + 27a b c d + 27a b c d - 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ +-+ +-+ \|c \|b x + a
+--R - 48a b c d\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (14a b d + 14b c d)x + 3a d + 38a b c d + 3b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 24b d\|b \|d
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1000
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 1000
+--m0:=a0-r0
+--E 194
+
+--S 195 of 1000
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^2
+--R
+--R
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R (1) -------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 1000
+r0:=-(a+b*x)^(3/2)*(c+d*x)^(3/2)/x-3*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+3/4*(b^2*c^2+6*a*b*c*d+a^2*d^2)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))+_
+ 3/2*b*(c+d*x)^(3/2)*sqrt(a+b*x)+3/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d + 18a b c d + 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ +-+ +-+ \|c \|b x + a
+--R (- 12a d - 12b c)x\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 +-+ +-+ +-------+ +-------+
+--R (2b d x + (5a d + 5b c)x - 4a c)\|b \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 4x\|b \|d
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1000
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 1000
+--m0:=a0-r0
+--E 199
+
+--S 200 of 1000
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^3
+--R
+--R
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R (1) -------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 1000
+r0:=-1/2*(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^2-3/4*(b^2*c^2+6*a*b*c*d+a^2*d^2)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(sqrt(a)*sqrt(c))+_
+ 3*(b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(b)*sqrt(d)-3/4*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x)+_
+ 3/4*d*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/c
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R (12a d + 12b c)x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 3a d - 18a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 +-+ +-+ +-------+ +-------+
+--R (4b d x + (- 5a d - 5b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4x \|a \|c
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 1000
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 1000
+--m0:=a0-r0
+--E 204
+
+--S 205 of 1000
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^4
+--R
+--R
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R (1) -------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 1000
+r0:=-1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^3+1/8*(b*c+a*d)*(b^2*c^2-_
+ 10*a*b*c*d+a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(3/2)*c^(3/2))+2*b^(3/2)*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))-1/4*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (c*x^2)-1/8*(b^2*c/a+8*b*d-a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/x
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 48a b c d x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (3a d - 27a b c d - 27a b c d + 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((- 3a d - 38a b c d - 3b c )x + (- 14a c d - 14a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1000
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 1000
+--m0:=a0-r0
+--E 209
+
+--S 210 of 1000
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^5
+--R
+--R
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R (1) -------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1000
+r0:=-1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^4)-3/64*(b*c-a*d)^4*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-_
+ 1/32*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x^2)-1/8*(b*c-a*d)*_
+ (c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x^3)+3/64*(b*c-a*d)^3*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^2*c^2*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 3a d + 12a b c d - 18a b c d + 12a b c d - 3b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (3a d - 11a b c d - 11a b c d + 3b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (- 2a c d - 44a b c d - 2a b c )x + (- 24a c d - 24a b c )x - 16a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 4 +-+ +-+
+--R 64a c x \|a \|c
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1000
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 1000
+--m0:=a0-r0
+--E 214
+
+--S 215 of 1000
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^6
+--R
+--R
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R (1) -------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1000
+r0:=-1/5*(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^5+3/128*(b*c-a*d)^4*(b*c+a*d)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_
+ 3/40*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^4)-1/80*(b^2*c/a+12*b*d-_
+ 5*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/x^3+1/320*(b*c+a*d)*(5*b^2*c^2-_
+ 18*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^2)-_
+ 1/640*(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)*sqrt(c+d*x)/(a^3*c^3*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5
+--R (15a d - 45a b c d + 30a b c d + 30a b c d - 45a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 15a d + 40a b c d - 18a b c d + 40a b c d - 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (10a c d - 26a b c d - 26a b c d + 10a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2 4 3 3 4
+--R (- 8a c d - 272a b c d - 8a b c )x + (- 176a c d - 176a b c )x
+--R +
+--R 4 4
+--R - 128a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 3 5 +-+ +-+
+--R 640a c x \|a \|c
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1000
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 1000
+--m0:=a0-r0
+--E 219
+
+--S 220 of 1000
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 1000
+t0:=x^2*(a+b*x)^(3/2)*(c+d*x)^(5/2)
+--R
+--R
+--R (1)
+--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 221
+
+--S 222 of 1000
+r0:=1/192*(b*c-a*d)*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*(a+b*x)^(5/2)*_
+ (c+d*x)^(3/2)/(b^4*d^2)+1/120*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*_
+ (a+b*x)^(5/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/84*(7*b*c+9*a*d)*_
+ (a+b*x)^(5/2)*(c+d*x)^(7/2)/(b^2*d^2)+1/7*x*(a+b*x)^(5/2)*_
+ (c+d*x)^(7/2)/(b*d)+1/1024*(b*c-a*d)^5*(5*b^2*c^2+10*a*b*c*d+_
+ 9*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(11/2)*d^(9/2))+1/1536*(b*c-a*d)^3*(5*b^2*c^2+10*a*b*c*d+_
+ 9*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^5*d^3)+1/384*(b*c-a*d)^2*_
+ (5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^5*d^2)-_
+ 1/1024*(b*c-a*d)^4*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^5*d^4)
+--R
+--R
+--R (2)
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R - 945a d + 3675a b c d - 4725a b c d + 1575a b c d + 525a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R 945a b c d - 1575a b c d + 525b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 6 6 6 5 6 6 5 5
+--R 15360b d x + (19200a b d + 37120b c d )x
+--R +
+--R 2 4 6 5 5 6 2 4 4
+--R (384a b d + 48640a b c d + 23680b c d )x
+--R +
+--R 3 3 6 2 4 5 5 2 4 6 3 3 3
+--R (- 432a b d + 1488a b c d + 33520a b c d + 240b c d )x
+--R +
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2
+--R (504a b d - 1744a b c d + 1824a b c d + 720a b c d - 280b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3
+--R - 630a b d + 2198a b c d - 2332a b c d + 300a b c d
+--R +
+--R 5 4 2 6 5
+--R - 910a b c d + 350b c d
+--R *
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 945a d - 3360a b c d + 3689a b c d - 600a b c d - 525a b c d
+--R +
+--R 5 5 6 6
+--R 1400a b c d - 525b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 5 4 +-+ +-+
+--R 107520b d \|b \|d
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 1000
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 1000
+--m0:=a0-r0
+--E 224
+
+--S 225 of 1000
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 1000
+t0:=x*(a+b*x)^(3/2)*(c+d*x)^(5/2)
+--R
+--R
+--R (1)
+--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 226
+
+--S 227 of 1000
+r0:=-1/96*(b*c-a*d)*(5*b*c+7*a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^3*d)-_
+ 1/60*(5*b*c+7*a*d)*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b^2*d)+_
+ 1/6*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(b*d)-1/512*(b*c-a*d)^5*_
+ (5*b*c+7*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(9/2)*d^(7/2))-1/768*(b*c-a*d)^3*(5*b*c+7*a*d)*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(b^4*d^2)-1/192*(b*c-a*d)^2*(5*b*c+7*a*d)*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b^4*d)+1/512*(b*c-a*d)^4*(5*b*c+7*a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^4*d^3)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 105a d - 450a b c d + 675a b c d - 300a b c d - 225a b c d
+--R +
+--R 5 5 6 6
+--R 270a b c d - 75b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 5 5 4 5 5 4 4
+--R 1280b d x + (1664a b d + 3200b c d )x
+--R +
+--R 2 3 5 4 4 5 2 3 3
+--R (48a b d + 4448a b c d + 2160b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5 3 2 2
+--R (- 56a b d + 216a b c d + 3384a b c d + 40b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4
+--R (70a b d - 272a b c d + 348a b c d + 160a b c d - 50b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 105a d + 415a b c d - 546a b c d + 150a b c d - 245a b c d
+--R +
+--R 5 5
+--R 75b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 3 +-+ +-+
+--R 7680b d \|b \|d
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1000
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 1000
+--m0:=a0-r0
+--E 229
+
+--S 230 of 1000
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)
+--R
+--R
+--R (1)
+--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 231
+
+--S 232 of 1000
+r0:=1/8*(b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/b^2+1/5*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)/b+3/128*(b*c-a*d)^5*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))+1/64*(b*c-a*d)^3*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d)+1/16*(b*c-a*d)^2*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/b^3-3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 15a d + 75a b c d - 150a b c d + 150a b c d - 75a b c d
+--R +
+--R 5 5
+--R 15b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 128b d x + (176a b d + 336b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (8a b d + 512a b c d + 248b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (- 10a b d + 46a b c d + 466a b c d + 10b c d)x + 15a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 70a b c d + 128a b c d + 70a b c d - 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 2 +-+ +-+
+--R 640b d \|b \|d
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 1000
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 1000
+--m0:=a0-r0
+--E 234
+
+--S 235 of 1000
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1000
+r0:=1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)-2*a^(3/2)*c^(5/2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))-1/64*(5*b^4*c^4-60*a*b^3*c^3*d-_
+ 90*a^2*b^2*c^2*d^2+20*a^3*b*c*d^3-3*a^4*d^4)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/96*(50*a*c-_
+ 5*b*c^2/d+3*a^2*d/b)*(c+d*x)^(3/2)*sqrt(a+b*x)+1/24*(5*b*c+3*a*d)*_
+ (c+d*x)^(5/2)*sqrt(a+b*x)/d-1/64*(5*b^3*c^3-55*a*b^2*c^2*d-_
+ 17*a^2*b*c*d^2+3*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (9a d - 60a b c d + 270a b c d + 180a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R - 384a b c d\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (72a b d + 136b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2 2 2
+--R (6a b d + 244a b c d + 118b c d)x - 9a d + 57a b c d + 337a b c d
+--R +
+--R 3 3
+--R 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 192b d\|b \|d
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 1000
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 1000
+--m0:=a0-r0
+--E 239
+
+--S 240 of 1000
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^2
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 1000
+r0:=-(a+b*x)^(3/2)*(c+d*x)^(5/2)/x-c^(3/2)*(3*b*c+5*a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+1/8*(5*b^3*c^3+45*a*_
+ b^2*c^2*d+15*a^2*b*c*d^2-a^3*d^3)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+1/12*(5*b*c+19*a*d)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)+4/3*b*(c+d*x)^(5/2)*sqrt(a+b*x)+_
+ 1/8*(5*b^2*c^2+26*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/b
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 3a d + 45a b c d + 135a b c d + 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R (- 120a b c d - 72b c )x\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 3 2 2 2 2 2 2 2
+--R 8b d x + (14a b d + 26b c d)x + (3a d + 68a b c d + 33b c )x
+--R +
+--R 2
+--R - 24a b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 24b x\|b \|d
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 1000
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 1000
+--m0:=a0-r0
+--E 244
+
+--S 245 of 1000
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^3
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1000
+r0:=-1/2*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^2-3/4*(b^2*c^2+10*a*b*c*d+_
+ 5*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(c)/sqrt(a)+3/4*(5*b^2*c^2+10*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)+1/4*d*_
+ (7*b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/c-1/4*(3*b*c+5*a*d)*_
+ (c+d*x)^(5/2)*sqrt(a+b*x)/(c*x)+3*d*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|d \|b x + a
+--R (3a d + 30a b c d + 15b c )x \|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a
+--R (- 15a d - 30a b c d - 3b c )x \|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2b d x + (5a d + 9b c d)x + (- 9a c d - 5b c )x - 2a c )\|a \|b
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4x \|a \|b
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1000
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 1000
+--m0:=a0-r0
+--E 249
+
+--S 250 of 1000
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^4
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1000
+r0:=-1/3*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^3+d^(3/2)*(5*b*c+3*a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_
+ 1/8*(b^3*c^3-15*a*b^2*c^2*d-45*a^2*b*c*d^2-5*a^3*d^3)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-_
+ 1/24*(3*b^2*c/a+40*b*d+5*a*d^2/c)*(c+d*x)^(3/2)*sqrt(a+b*x)/x-_
+ 1/12*(3*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^2)+_
+ 1/8*d*(b^2*c^2+26*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 3 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R (72a d + 120a b c d)x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 15a d - 135a b c d - 45a b c d + 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 2 2
+--R 24a b d x + (- 33a d - 68a b c d - 3b c )x
+--R +
+--R 2 2 2 2
+--R (- 26a c d - 14a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24a x \|a \|c
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 1000
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 1000
+--m0:=a0-r0
+--E 254
+
+--S 255 of 1000
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^5
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1000
+r0:=-1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^4-1/64*(3*b^4*c^4-20*a*b^3*c^3*d+_
+ 90*a^2*b^2*c^2*d^2+60*a^3*b*c*d^3-5*a^4*d^4)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(3/2))+2*b^(3/2)*_
+ d^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-_
+ 1/96*(3*b^2*c/a+50*b*d-5*a*d^2/c)*(c+d*x)^(3/2)*sqrt(a+b*x)/x^2-_
+ 1/24*(3*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+_
+ 1/64*(3*b^3*c^3-17*a*b^2*c^2*d-55*a^2*b*c*d^2+5*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 4 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 384a b c d x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d - 180a b c d - 270a b c d + 60a b c d - 9b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 15a d - 337a b c d - 57a b c d + 9b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 118a c d - 244a b c d - 6a b c )x + (- 136a c d - 72a b c )x
+--R +
+--R 3 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 1000
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 1000
+--m0:=a0-r0
+--E 259
+
+--S 260 of 1000
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^6
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 1000
+r0:=-1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(c*x^5)+3/128*(b*c-a*d)^5*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(5/2))+_
+ 1/64*(b*c-a*d)^3*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c^2*x^2)-_
+ 1/80*(b*c-a*d)^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c^2*x^3)-_
+ 3/40*(b*c-a*d)*(c+d*x)^(7/2)*sqrt(a+b*x)/(c^2*x^4)-_
+ 3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 15a d + 75a b c d - 150a b c d + 150a b c d - 75a b c d
+--R +
+--R 5 5
+--R 15b c
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d - 70a b c d - 128a b c d + 70a b c d - 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (- 10a c d - 466a b c d - 46a b c d + 10a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2 4 3 3 4
+--R (- 248a c d - 512a b c d - 8a b c )x + (- 336a c d - 176a b c )x
+--R +
+--R 4 4
+--R - 128a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 2 5 +-+ +-+
+--R 640a c x \|a \|c
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 1000
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 1000
+--m0:=a0-r0
+--E 264
+
+--S 265 of 1000
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 1000
+t0:=(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^7
+--R
+--R
+--R (1)
+--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 --------------------------------------------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1000
+r0:=-1/6*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^6-1/512*(b*c-a*d)^5*(7*b*c+5*a*d)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-_
+ 1/480*(3*b^2*c/a+70*b*d-25*a*d^2/c)*(c+d*x)^(3/2)*sqrt(a+b*x)/x^4-_
+ 1/60*(3*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^5)+_
+ 1/960*(b*c-5*a*d)*(7*b^2*c^2+14*a*b*c*d-5*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^2*c*x^3)-1/3840*(35*b^4*c^4-136*a*b^3*c^3*d+_
+ 174*a^2*b^2*c^2*d^2+80*a^3*b*c*d^3-25*a^4*d^4)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^3*c^2*x^2)+1/7680*(105*b^5*c^5-415*a*b^4*c^4*d+_
+ 546*a^2*b^3*c^3*d^2-150*a^3*b^2*c^2*d^3+245*a^4*b*c*d^4-75*a^5*d^5)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^3*x)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 75a d - 270a b c d + 225a b c d + 300a b c d - 675a b c d
+--R +
+--R 5 5 6 6
+--R 450a b c d - 105b c
+--R *
+--R +-+ +-------+
+--R 6 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 75a d + 245a b c d - 150a b c d + 546a b c d - 415a b c d
+--R +
+--R 5 5
+--R 105b c
+--R *
+--R 5
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4
+--R (50a c d - 160a b c d - 348a b c d + 272a b c d - 70a b c )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 3
+--R (- 40a c d - 3384a b c d - 216a b c d + 56a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5 2
+--R (- 2160a c d - 4448a b c d - 48a b c )x
+--R +
+--R 5 4 4 5 5 5
+--R (- 3200a c d - 1664a b c )x - 1280a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 4 3 6 +-+ +-+
+--R 7680a c x \|a \|c
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 1000
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 1000
+--m0:=a0-r0
+--E 269
+
+--S 270 of 1000
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 1000
+t0:=x^2*(a+b*x)^(3/2)/sqrt(c+d*x)
+--R
+--R
+--R 3 2 +-------+
+--R (b x + a x )\|b x + a
+--R (1) -----------------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1000
+r0:=1/64*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(9/2))+_
+ 1/96*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(b^2*d^3)-1/24*(7*b*c+3*a*d)*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b^2*d^2)+1/4*x*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)-_
+ 1/64*(b*c-a*d)*(35*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^4)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (9a d + 12a b c d + 54a b c d - 180a b c d + 105b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (72a b d - 56b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2 2 2
+--R (6a b d - 92a b c d + 70b c d)x - 9a d - 15a b c d + 145a b c d
+--R +
+--R 3 3
+--R - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 4 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 1000
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 1000
+--m0:=a0-r0
+--E 274
+
+--S 275 of 1000
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 1000
+t0:=x*(a+b*x)^(3/2)/sqrt(c+d*x)
+--R
+--R
+--R 2 +-------+
+--R (b x + a x)\|b x + a
+--R (1) ----------------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1000
+r0:=-1/8*(b*c-a*d)^2*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(3/2)*d^(7/2))-1/12*(5*b*c+a*d)*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(b*d^2)+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)+_
+ 1/8*(b*c-a*d)*(5*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^3)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 3a d - 9a b c d + 27a b c d - 15b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (14a b d - 10b c d)x + 3a d - 22a b c d + 15b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24b d \|b \|d
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 1000
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 1000
+--m0:=a0-r0
+--E 279
+
+--S 280 of 1000
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 1000
+t0:=(a+b*x)^(3/2)/sqrt(c+d*x)
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 1000
+r0:=3/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (d^(5/2)*sqrt(b))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/d-3/4*(b*c-a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/d^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d - 6a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (2b d x + 5a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4d \|b \|d
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 1000
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 1000
+--m0:=a0-r0
+--E 284
+
+--S 285 of 1000
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 1000
+t0:=(a+b*x)^(3/2)/(x*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R +-------+
+--R x\|d x + c
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 1000
+r0:=-(b*c-3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(b)/d^(3/2)-2*a^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/sqrt(c)+b*sqrt(a+b*x)*sqrt(c+d*x)/d
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ \|d \|b x + a
+--R (3a d - b c)\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ \|c \|b x + a +-+ +-+ +-------+ +-------+
+--R - 2a d\|a \|d atanh(--------------) + b\|c \|d \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|a \|d x + c
+--R /
+--R +-+ +-+
+--R d\|c \|d
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 1000
+--a0:=integrate(t0,x)
+--E 288
+
+--S 289 of 1000
+--m0:=a0-r0
+--E 289
+
+--S 290 of 1000
+--d0:=D(m0,x)
+--E 290
+
+)clear all
+
+--S 291 of 1000
+t0:=(a+b*x)^(3/2)/(x^2*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R 2 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 1000
+r0:=-(3*b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(a)/c^(3/2)+2*b^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/sqrt(d)-(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x)+_
+ b*sqrt(a+b*x)*sqrt(c+d*x)/c
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ \|d \|b x + a
+--R 2b c x\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ \|c \|b x + a +-+ +-+ +-------+ +-------+
+--R (a d - 3b c)x\|a \|d atanh(--------------) - a\|c \|d \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|a \|d x + c
+--R /
+--R +-+ +-+
+--R c x\|c \|d
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1000
+--a0:=integrate(t0,x)
+--E 293
+
+--S 294 of 1000
+--m0:=a0-r0
+--E 294
+
+--S 295 of 1000
+--d0:=D(m0,x)
+--E 295
+
+)clear all
+
+--S 296 of 1000
+t0:=(a+b*x)^(3/2)/(x^3*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R 3 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1000
+r0:=-3/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (c^(5/2)*sqrt(a))-1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^2)-_
+ 3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 3a d + 6a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R ((3a d - 5b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4c x \|a \|c
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 1000
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 1000
+--m0:=a0-r0
+--E 299
+
+--S 300 of 1000
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 1000
+t0:=(a+b*x)^(3/2)/(x^4*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R 4 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 1000
+r0:=1/8*(b*c-a*d)^2*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(3/2)*c^(7/2))-1/3*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (c*x^3)-1/12*(3*b*c-5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x^2)-_
+ 1/24*(3*b^2*c/a-22*b*d+15*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (15a d - 27a b c d + 9a b c d + 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((- 15a d + 22a b c d - 3b c )x + (10a c d - 14a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1000
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 1000
+--m0:=a0-r0
+--E 304
+
+--S 305 of 1000
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 1000
+t0:=(a+b*x)^(3/2)/(x^5*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R 5 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1000
+r0:=-1/64*(b*c-a*d)^2*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(9/2))-_
+ 1/4*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^4)-1/24*(3*b*c-7*a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x^3)-1/96*(3*b^2*c/a-46*b*d+_
+ 35*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x^2)+1/192*(9*b^3*c^3+_
+ 15*a*b^2*c^2*d-145*a^2*b*c*d^2+105*a^3*d^3)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^2*c^4*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 105a d + 180a b c d - 54a b c d - 12a b c d - 9b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (105a d - 145a b c d + 15a b c d + 9b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (- 70a c d + 92a b c d - 6a b c )x + (56a c d - 72a b c )x - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 4 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1000
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 1000
+--m0:=a0-r0
+--E 309
+
+--S 310 of 1000
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 1000
+t0:=x^2*(a+b*x)^(3/2)/(c+d*x)^(3/2)
+--R
+--R
+--R 3 2 +-------+
+--R (b x + a x )\|b x + a
+--R (1) -----------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1000
+r0:=-1/8*(b*c-a*d)*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(9/2))+_
+ 2*c^2*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+_
+ 1/12*(10*a*c-35*b*c^2/d+a^2*d/b)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (d^2*(b*c-a*d))+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d^2)+_
+ 1/8*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-------+
+--R (- 3a d - 27a b c d + 135a b c d - 105b c )\|d x + c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 3 3 3 2 2 2 2 3 2 2 2
+--R 8b d x + (14a b d - 14b c d )x + (3a d - 38a b c d + 35b c d)x
+--R +
+--R 2 2 2 2 3
+--R 3a c d - 100a b c d + 105b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 4 +-+ +-+ +-------+
+--R 24b d \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 1000
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 1000
+--m0:=a0-r0
+--E 314
+
+--S 315 of 1000
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 1000
+t0:=x*(a+b*x)^(3/2)/(c+d*x)^(3/2)
+--R
+--R
+--R 2 +-------+
+--R (b x + a x)\|b x + a
+--R (1) ----------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 1000
+r0:=3/4*(b*c-a*d)*(5*b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(d^(7/2)*sqrt(b))-2*c*(a+b*x)^(5/2)/(d*(b*c-a*d)*_
+ sqrt(c+d*x))+1/2*(5*b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (d^2*(b*c-a*d))-3/4*(5*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^3
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ \|d \|b x + a
+--R (3a d - 18a b c d + 15b c )\|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+
+--R (2b d x + (5a d - 5b c d)x + 13a c d - 15b c )\|b \|d \|b x + a
+--R /
+--R 3 +-+ +-+ +-------+
+--R 4d \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1000
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 1000
+--m0:=a0-r0
+--E 319
+
+--S 320 of 1000
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 1000
+t0:=(a+b*x)^(3/2)/(c+d*x)^(3/2)
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 1000
+r0:=-3*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(b)/d^(5/2)-2*(a+b*x)^(3/2)/(d*sqrt(c+d*x))+3*b*_
+ sqrt(a+b*x)*sqrt(c+d*x)/d^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-------+ \|d \|b x + a
+--R (3a d - 3b c)\|b \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R (b d x - 2a d + 3b c)\|d \|b x + a
+--R /
+--R 2 +-+ +-------+
+--R d \|d \|d x + c
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1000
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 1000
+--m0:=a0-r0
+--E 324
+
+--S 325 of 1000
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 1000
+t0:=(a+b*x)^(3/2)/(x*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) ----------------------
+--R 2 +-------+
+--R (d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 1000
+r0:=-2*a^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(3/2)+_
+ 2*b^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ d^(3/2)+2*(a+b*x)^(3/2)/(c*sqrt(c+d*x))-2*b*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(c*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ +-------+ \|d \|b x + a
+--R 2b c\|b \|c \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ +-------+ \|c \|b x + a
+--R - 2a d\|a \|d \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+
+--R (2a d - 2b c)\|c \|d \|b x + a
+--R /
+--R +-+ +-+ +-------+
+--R c d\|c \|d \|d x + c
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 1000
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 1000
+--m0:=a0-r0
+--E 329
+
+--S 330 of 1000
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 1000
+t0:=(a+b*x)^(3/2)/(x^2*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -----------------------
+--R 3 2 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 1000
+r0:=-3*(b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(a)/c^(5/2)-(a+b*x)^(3/2)/(c*x*sqrt(c+d*x))+3*(b*c-a*d)*_
+ sqrt(a+b*x)/(c^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-------+ \|c \|b x + a
+--R (3a d - 3b c)x\|a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-------+
+--R ((- 3a d + 2b c)x - a c)\|c \|b x + a
+--R /
+--R 2 +-+ +-------+
+--R c x\|c \|d x + c
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1000
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 1000
+--m0:=a0-r0
+--E 334
+
+--S 335 of 1000
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 1000
+t0:=(a+b*x)^(3/2)/(x^3*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -----------------------
+--R 4 3 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 1000
+r0:=-3/4*(b*c-5*a*d)*(b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(c^(7/2)*sqrt(a))-1/2*(a+b*x)^(3/2)/_
+ (c*x^2*sqrt(c+d*x))-1/4*d*(13*b*c-15*a*d)*sqrt(a+b*x)/_
+ (c^3*sqrt(c+d*x))-1/4*(3*b*c-5*a*d)*sqrt(a+b*x)/(c^2*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-------+ \|c \|b x + a
+--R (- 15a d + 18a b c d - 3b c )x \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+
+--R ((15a d - 13b c d)x + (5a c d - 5b c )x - 2a c )\|a \|c \|b x + a
+--R /
+--R 3 2 +-+ +-+ +-------+
+--R 4c x \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1000
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 1000
+--m0:=a0-r0
+--E 339
+
+--S 340 of 1000
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 1000
+t0:=(a+b*x)^(3/2)/(x^4*(c+d*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) -----------------------
+--R 5 4 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 1000
+r0:=1/8*(b*c-a*d)*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(9/2))-_
+ 1/3*(a+b*x)^(3/2)/(c*x^3*sqrt(c+d*x))-1/24*d*(3*b^2*c^2-_
+ 100*a*b*c*d+105*a^2*d^2)*sqrt(a+b*x)/(a*c^4*sqrt(c+d*x))-_
+ 1/12*(3*b*c-7*a*d)*sqrt(a+b*x)/(c^2*x^2*sqrt(c+d*x))-_
+ 1/24*(3*b*c-35*a*d)*(b*c-a*d)*sqrt(a+b*x)/(a*c^3*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 3 +-------+
+--R (105a d - 135a b c d + 27a b c d + 3b c )x \|d x + c
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 3
+--R (- 105a d + 100a b c d - 3b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3 2 3
+--R (- 35a c d + 38a b c d - 3b c )x + (14a c d - 14a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 4 3 +-+ +-+ +-------+
+--R 24a c x \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1000
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 1000
+--m0:=a0-r0
+--E 344
+
+--S 345 of 1000
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 1000
+t0:=x^2*(a+b*x)^(3/2)/(c+d*x)^(5/2)
+--R
+--R
+--R 3 2 +-------+
+--R (b x + a x )\|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1000
+r0:=2/3*c^2*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))+_
+ 1/4*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(9/2)*sqrt(b))-_
+ 4/3*c*(4*b*c-3*a*d)*(a+b*x)^(5/2)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))+_
+ 1/6*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (d^3*(b*c-a*d)^2)-1/4*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(d^4*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 3
+--R ((9a d - 90a b c d + 105b c d)x + 9a c d - 90a b c d + 105b c )
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 2 2 2 2
+--R 6b d x + (15a d - 21b c d )x + (78a c d - 140b c d)x + 55a c d
+--R +
+--R 3
+--R - 105b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 5 4 +-+ +-+ +-------+
+--R (12d x + 12c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1000
+--a0:=integrate(t0,x)
+--E 348
+
+--S 349 of 1000
+--m0:=a0-r0
+--E 349
+
+--S 350 of 1000
+--d0:=D(m0,x)
+--E 350
+
+)clear all
+
+--S 351 of 1000
+t0:=x*(a+b*x)^(3/2)/(c+d*x)^(5/2)
+--R
+--R
+--R 2 +-------+
+--R (b x + a x)\|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1000
+r0:=-2/3*c*(a+b*x)^(5/2)/(d*(b*c-a*d)*(c+d*x)^(3/2))-(5*b*c-3*a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(7/2)-_
+ 2/3*(5*b*c-3*a*d)*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+_
+ b*(5*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(d^3*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-------+ \|d \|b x + a
+--R ((9a d - 15b c d)x + 9a c d - 15b c )\|b \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-------+
+--R (3b d x + (- 6a d + 20b c d)x - 4a c d + 15b c )\|d \|b x + a
+--R /
+--R 4 3 +-+ +-------+
+--R (3d x + 3c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 1000
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 1000
+--m0:=a0-r0
+--E 354
+
+--S 355 of 1000
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 1000
+t0:=(a+b*x)^(3/2)/(c+d*x)^(5/2)
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1000
+r0:=-2/3*(a+b*x)^(3/2)/(d*(c+d*x)^(3/2))+2*b^(3/2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(5/2)-2*b*sqrt(a+b*x)/_
+ (d^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-------+ \|d \|b x + a
+--R (6b d x + 6b c)\|b \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R (- 8b d x - 2a d - 6b c)\|d \|b x + a
+--R /
+--R 3 2 +-+ +-------+
+--R (3d x + 3c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 1000
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 1000
+--m0:=a0-r0
+--E 359
+
+--S 360 of 1000
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 1000
+t0:=(a+b*x)^(3/2)/(x*(c+d*x)^(5/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) --------------------------------
+--R 2 3 2 2 +-------+
+--R (d x + 2c d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1000
+r0:=2/3*(a+b*x)^(3/2)/(c*(c+d*x)^(3/2))-2*a^(3/2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(5/2)+2*a*sqrt(a+b*x)/_
+ (c^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-------+ \|c \|b x + a
+--R (- 6a d x - 6a c)\|a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-------+
+--R ((6a d + 2b c)x + 8a c)\|c \|b x + a
+--R /
+--R 2 3 +-+ +-------+
+--R (3c d x + 3c )\|c \|d x + c
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 1000
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 1000
+--m0:=a0-r0
+--E 364
+
+--S 365 of 1000
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 1000
+t0:=(a+b*x)^(3/2)/(x^2*(c+d*x)^(5/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) ---------------------------------
+--R 2 4 3 2 2 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1000
+r0:=-(a+b*x)^(3/2)/(c*x*(c+d*x)^(3/2))-(3*b*c-5*a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(7/2)+5/3*(b*c-a*d)*_
+ sqrt(a+b*x)/(c^2*(c+d*x)^(3/2))+1/3*(4*b*c-15*a*d)*sqrt(a+b*x)/_
+ (c^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+ +-------+
+--R ((15a d - 9b c d)x + (15a c d - 9b c )x)\|a \|d x + c
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-------+
+--R ((- 15a d + 4b c d)x + (- 20a c d + 6b c )x - 3a c )\|c \|b x + a
+--R /
+--R 3 2 4 +-+ +-------+
+--R (3c d x + 3c x)\|c \|d x + c
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 1000
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 1000
+--m0:=a0-r0
+--E 369
+
+--S 370 of 1000
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 1000
+t0:=(a+b*x)^(3/2)/(x^3*(c+d*x)^(5/2))
+--R
+--R
+--R +-------+
+--R (b x + a)\|b x + a
+--R (1) ---------------------------------
+--R 2 5 4 2 3 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1000
+r0:=-1/2*(a+b*x)^(3/2)/(c*x^2*(c+d*x)^(3/2))-1/4*(3*b^2*c^2-30*a*b*c*d+_
+ 35*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (c^(9/2)*sqrt(a))-1/12*d*(23*b*c-35*a*d)*sqrt(a+b*x)/_
+ (c^3*(c+d*x)^(3/2))-1/4*(3*b*c-7*a*d)*sqrt(a+b*x)/(c^2*x*(c+d*x)^(3/2))-_
+ 5/12*d*(11*b*c-21*a*d)*sqrt(a+b*x)/(c^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 3
+--R (- 105a d + 90a b c d - 9b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (- 105a c d + 90a b c d - 9b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 2 3 2 2 2
+--R (105a d - 55b c d )x + (140a c d - 78b c d)x
+--R +
+--R 2 3 3
+--R (21a c d - 15b c )x - 6a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 4 3 5 2 +-+ +-+ +-------+
+--R (12c d x + 12c x )\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 1000
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 1000
+--m0:=a0-r0
+--E 374
+
+--S 375 of 1000
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 1000
+t0:=x^2*(a+b*x)^(5/2)*sqrt(c+d*x)
+--R
+--R
+--R 2 4 3 2 2 +-------+ +-------+
+--R (1) (b x + 2a b x + a x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 1000
+r0:=-1/60*(9*b*c+5*a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^2*d^2)+_
+ 1/6*x*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b*d)-1/512*(b*c-a*d)^4*_
+ (21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(11/2))-1/768*(b*c-a*d)^2*_
+ (21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (b^3*d^4)+1/960*(b*c-a*d)*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*_
+ (a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d^3)+1/160*(21*b^2*c^2+_
+ 14*a*b*c*d+5*a^2*d^2)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^3*d^2)+_
+ 1/512*(b*c-a*d)^3*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^5)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 75a d + 90a b c d + 75a b c d + 300a b c d - 1125a b c d
+--R +
+--R 5 5 6 6
+--R 1050a b c d - 315b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 5 5 4 5 5 4 4
+--R 1280b d x + (3200a b d + 128b c d )x
+--R +
+--R 2 3 5 4 4 5 2 3 3
+--R (2160a b d + 416a b c d - 144b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5 3 2 2
+--R (40a b d + 408a b c d - 488a b c d + 168b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4
+--R (- 50a b d + 40a b c d - 524a b c d + 616a b c d - 210b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R 75a d - 65a b c d - 90a b c d + 838a b c d - 945a b c d + 315b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 5 +-+ +-+
+--R 7680b d \|b \|d
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 1000
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 1000
+--m0:=a0-r0
+--E 379
+
+--S 380 of 1000
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 1000
+t0:=x*(a+b*x)^(5/2)*sqrt(c+d*x)
+--R
+--R
+--R 2 3 2 2 +-------+ +-------+
+--R (1) (b x + 2a b x + a x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 1000
+r0:=1/5*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b*d)+1/128*(b*c-a*d)^4*(7*b*c+3*a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(9/2))+_
+ 1/192*(b*c-a*d)^2*(7*b*c+3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^3)-_
+ 1/240*(b*c-a*d)*(7*b*c+3*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d^2)-_
+ 1/40*(7*b*c+3*a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^2*d)-_
+ 1/128*(b*c-a*d)^3*(7*b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^4)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 45a d - 75a b c d - 150a b c d + 450a b c d - 375a b c d
+--R +
+--R 5 5
+--R 105b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 384b d x + (1008a b d + 48b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (744a b d + 176a b c d - 56b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (30a b d + 218a b c d - 222a b c d + 70b c d)x - 45a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R 60a b c d - 346a b c d + 340a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 4 +-+ +-+
+--R 1920b d \|b \|d
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 1000
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 1000
+--m0:=a0-r0
+--E 384
+
+--S 385 of 1000
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (1) (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1000
+r0:=-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(3/2)*d^(7/2))-5/96*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (b*d^2)+1/24*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)+_
+ 1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/b+5/64*(b*c-a*d)^3*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b*d^3)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (136a b d + 8b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2 2 2
+--R (118a b d + 36a b c d - 10b c d)x + 15a d + 73a b c d - 55a b c d
+--R +
+--R 3 3
+--R 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1000
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 1000
+--m0:=a0-r0
+--E 389
+
+--S 390 of 1000
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)/x
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 1000
+r0:=1/8*(b^3*c^3-5*a*b^2*c^2*d+15*a^2*b*c*d^2+5*a^3*d^3)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(5/2)*sqrt(b))-_
+ 2*a^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(c)+1/12*(b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d+_
+ 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)-1/8*(b*c-5*a*d)*(b*c+a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/d^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (15a d + 45a b c d - 15a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R - 48a d \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (26a b d + 2b c d)x + 33a d + 14a b c d - 3b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 24d \|b \|d
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1000
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 1000
+--m0:=a0-r0
+--E 394
+
+--S 395 of 1000
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)/x^2
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 1000
+r0:=-1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(3/2)-a^(3/2)*(5*b*c+a*d)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(c)+3/2*b*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)-(a+b*x)^(5/2)*sqrt(c+d*x)/x+_
+ 1/4*b*(b*c+11*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-+ \|d \|b x + a
+--R (15a d + 10a b c d - b c )x\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|c \|b x + a
+--R (- 4a d - 20a b c d)x\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+ +-------+
+--R (2b d x + (9a b d + b c)x - 4a d)\|c \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 4d x\|c \|d
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1000
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 1000
+--m0:=a0-r0
+--E 399
+
+--S 400 of 1000
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)/x^3
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 1000
+r0:=-1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(3/2)+b^(3/2)*(b*c+5*a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(d)-_
+ 1/4*(5*b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x)-1/2*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/x^2+1/4*b*(11*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/c
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 +-+ +-+ \|d \|b x + a
+--R (20a b c d + 4b c )x \|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a
+--R (a d - 10a b c d - 15b c )x \|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+ +-------+
+--R (4b c x + (- a d - 9a b c)x - 2a c)\|c \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4c x \|c \|d
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1000
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 1000
+--m0:=a0-r0
+--E 404
+
+--S 405 of 1000
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)/x^4
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 1000
+r0:=-1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*sqrt(a))+_
+ 2*b^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(d)-1/12*(5*b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^2)-_
+ 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/x^3-1/8*(5*b*c-a*d)*(b*c+a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 3 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 48b c x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 3a d + 15a b c d - 45a b c d - 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((3a d - 14a b c d - 33b c )x + (- 2a c d - 26a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 24c x \|a \|c
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1000
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 1000
+--m0:=a0-r0
+--E 409
+
+--S 410 of 1000
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)/x^5
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1000
+r0:=-5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c^2*x^3)-1/4*(a+b*x)^(5/2)*_
+ (c+d*x)^(3/2)/(c*x^4)+5/64*(b*c-a*d)^4*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(7/2))-5/32*(b*c-a*d)^2*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/(c^3*x^2)-5/64*(b*c-a*d)^3*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a*c^3*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d - 60a b c d + 90a b c d - 60a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 15a d + 55a b c d - 73a b c d - 15b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (10a c d - 36a b c d - 118a b c )x + (- 8a c d - 136a b c )x - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1000
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 1000
+--m0:=a0-r0
+--E 414
+
+--S 415 of 1000
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 1000
+t0:=(a+b*x)^(5/2)*sqrt(c+d*x)/x^6
+--R
+--R
+--R 2 2 2 +-------+ +-------+
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R (1) ----------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 1000
+r0:=-1/128*(b*c-a*d)^4*(3*b*c+7*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(9/2))-1/40*(5*b*c+a*d)*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^4)-1/5*(a+b*x)^(5/2)*sqrt(c+d*x)/x^5-_
+ 1/240*(3*b*c-a*d)*(5*b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x^3)-_
+ 1/960*(15*b^3*c^3+109*a*b^2*c^2*d-111*a^2*b*c*d^2+35*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a*c^3*x^2)+1/1920*(45*b^4*c^4-_
+ 60*a*b^3*c^3*d+346*a^2*b^2*c^2*d^2-340*a^3*b*c*d^3+105*a^4*d^4)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^4*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 105a d + 375a b c d - 450a b c d + 150a b c d + 75a b c d
+--R +
+--R 5 5
+--R - 45b c
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (105a d - 340a b c d + 346a b c d - 60a b c d + 45b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (- 70a c d + 222a b c d - 218a b c d - 30a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2 4 3 3 4
+--R (56a c d - 176a b c d - 744a b c )x + (- 48a c d - 1008a b c )x
+--R +
+--R 4 4
+--R - 384a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 4 5 +-+ +-+
+--R 1920a c x \|a \|c
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 1000
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 1000
+--m0:=a0-r0
+--E 419
+
+--S 420 of 1000
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 1000
+t0:=x^2*(a+b*x)^(5/2)*(c+d*x)^(3/2)
+--R
+--R
+--R (1)
+--R 2 5 2 4 2 3 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 1000
+r0:=1/120*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/_
+ (b^3*d^2)-1/84*(9*b*c+7*a*d)*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b^2*d^2)+_
+ 1/7*x*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b*d)-1/1024*(b*c-a*d)^5*_
+ (9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(11/2))-1/1536*(b*c-a*d)^3*_
+ (9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (b^4*d^4)+1/1920*(b*c-a*d)^2*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*_
+ (a+b*x)^(5/2)*sqrt(c+d*x)/(b^4*d^3)+1/320*(b*c-a*d)*(9*b^2*c^2+_
+ 10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^4*d^2)+_
+ 1/1024*(b*c-a*d)^4*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^4*d^5)
+--R
+--R
+--R (2)
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R 525a d - 1575a b c d + 945a b c d + 525a b c d + 1575a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R - 4725a b c d + 3675a b c d - 945b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 6 6 6 5 6 6 5 5
+--R 15360b d x + (37120a b d + 19200b c d )x
+--R +
+--R 2 4 6 5 5 6 2 4 4
+--R (23680a b d + 48640a b c d + 384b c d )x
+--R +
+--R 3 3 6 2 4 5 5 2 4 6 3 3 3
+--R (240a b d + 33520a b c d + 1488a b c d - 432b c d )x
+--R +
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3
+--R - 280a b d + 720a b c d + 1824a b c d - 1744a b c d
+--R +
+--R 6 4 2
+--R 504b c d
+--R *
+--R 2
+--R x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3
+--R 350a b d - 910a b c d + 300a b c d - 2332a b c d
+--R +
+--R 5 4 2 6 5
+--R 2198a b c d - 630b c d
+--R *
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 525a d + 1400a b c d - 525a b c d - 600a b c d + 3689a b c d
+--R +
+--R 5 5 6 6
+--R - 3360a b c d + 945b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 5 +-+ +-+
+--R 107520b d \|b \|d
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1000
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 1000
+--m0:=a0-r0
+--E 424
+
+--S 425 of 1000
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 1000
+t0:=x*(a+b*x)^(5/2)*(c+d*x)^(3/2)
+--R
+--R
+--R (1)
+--R 2 4 2 3 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 1000
+r0:=-1/60*(7*b*c+5*a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^2*d)+1/6*_
+ (a+b*x)^(7/2)*(c+d*x)^(5/2)/(b*d)+1/512*(b*c-a*d)^5*(7*b*c+5*a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+_
+ 1/768*(b*c-a*d)^3*(7*b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^3)-_
+ 1/960*(b*c-a*d)^2*(7*b*c+5*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d^2)-_
+ 1/160*(b*c-a*d)*(7*b*c+5*a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^3*d)-_
+ 1/512*(b*c-a*d)^4*(7*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 75a d + 270a b c d - 225a b c d - 300a b c d + 675a b c d
+--R +
+--R 5 5 6 6
+--R - 450a b c d + 105b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 5 5 4 5 5 4 4
+--R 1280b d x + (3200a b d + 1664b c d )x
+--R +
+--R 2 3 5 4 4 5 2 3 3
+--R (2160a b d + 4448a b c d + 48b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5 3 2 2
+--R (40a b d + 3384a b c d + 216a b c d - 56b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4
+--R (- 50a b d + 160a b c d + 348a b c d - 272a b c d + 70b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R 75a d - 245a b c d + 150a b c d - 546a b c d + 415a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 4 +-+ +-+
+--R 7680b d \|b \|d
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 1000
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 1000
+--m0:=a0-r0
+--E 429
+
+--S 430 of 1000
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1000
+r0:=1/5*(a+b*x)^(7/2)*(c+d*x)^(3/2)/b-3/128*(b*c-a*d)^5*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))-1/64*(b*c-a*d)^3*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^2)+1/80*(b*c-a*d)^2*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b^2*d)+3/40*(b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/b^2+_
+ 3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (15a d - 75a b c d + 150a b c d - 150a b c d + 75a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 128b d x + (336a b d + 176b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (248a b d + 512a b c d + 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (10a b d + 466a b c d + 46a b c d - 10b c d)x - 15a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R 70a b c d + 128a b c d - 70a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 640b d \|b \|d
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1000
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 1000
+--m0:=a0-r0
+--E 434
+
+--S 435 of 1000
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)/x
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R -----------------------------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 1000
+r0:=1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/d+1/4*(a+b*x)^(5/2)*_
+ (c+d*x)^(3/2)-2*a^(5/2)*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))+1/64*(3*b^4*c^4-20*a*b^3*c^3*d+90*a^2*b^2*_
+ c^2*d^2+60*a^3*b*c*d^3-5*a^4*d^4)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))-1/32*(b*c-5*a*d)*_
+ (3*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/d^2+1/64*(3*b^3*c^3-_
+ 17*a*b^2*c^2*d+73*a^2*b*c*d^2+5*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d + 180a b c d + 270a b c d - 60a b c d + 9b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R - 384a b c d \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (136a b d + 72b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2
+--R (118a b d + 244a b c d + 6b c d)x + 15a d + 337a b c d
+--R +
+--R 2 2 3 3
+--R 57a b c d - 9b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 1000
+--m0:=a0-r0
+--E 439
+
+--S 440 of 1000
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^2
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R -----------------------------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 1000
+r0:=4/3*b*(a+b*x)^(3/2)*(c+d*x)^(3/2)-(a+b*x)^(5/2)*(c+d*x)^(3/2)/x-_
+ 1/8*(b^3*c^3-15*a*b^2*c^2*d-45*a^2*b*c*d^2-5*a^3*d^3)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(3/2)*_
+ sqrt(b))-a^(3/2)*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))*sqrt(c)+1/4*b*(b*c+7*a*d)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/d-1/8*(b^2*c^2-14*a*b*c*d-19*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/d
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (15a d + 135a b c d + 45a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R (- 72a d - 120a b c d)x\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 3 2 2 2 2 2 2 2
+--R 8b d x + (26a b d + 14b c d)x + (33a d + 68a b c d + 3b c )x
+--R +
+--R 2
+--R - 24a c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 24d x\|b \|d
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 1000
+--m0:=a0-r0
+--E 444
+
+--S 445 of 1000
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^3
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R -----------------------------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 1000
+r0:=-1/4*(5*b*c+3*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x)-1/2*(a+b*x)^(5/2)*_
+ (c+d*x)^(3/2)/x^2-3/4*(5*b^2*c^2+10*a*b*c*d+a^2*d^2)*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/sqrt(c)+_
+ 3/4*(b^2*c^2+10*a*b*c*d+5*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))*sqrt(b)/sqrt(d)+3/4*b*(3*b*c+a*d)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/c+3/4*(b^2*c^2+6*a*b*c*d+a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/c
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|d \|b x + a
+--R (15a d + 30a b c d + 3b c )x \|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a
+--R (- 3a d - 30a b c d - 15b c )x \|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2b d x + (9a b d + 5b c)x + (- 5a d - 9a b c)x - 2a c)\|c \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4x \|c \|d
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 1000
+--m0:=a0-r0
+--E 449
+
+--S 450 of 1000
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^4
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R -----------------------------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 1000
+r0:=-1/12*(5*b*c+3*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x^2)-_
+ 1/3*(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^3-1/8*(5*b^3*c^3+45*a*b^2*c^2*d+_
+ 15*a^2*b*c*d^2-a^3*d^3)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(c^(3/2)*sqrt(a))+b^(3/2)*(3*b*c+5*a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)-_
+ 1/8*(5*b^2*c^2+12*a*b*c*d-a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (c^2*x)+1/8*d*(19*b^2*c^2+14*a*b*c*d-a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/c^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 3 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R (120a b c d + 72b c )x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (3a d - 45a b c d - 135a b c d - 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 2 2
+--R 24b c d x + (- 3a d - 68a b c d - 33b c )x
+--R +
+--R 2 2 2 2
+--R (- 14a c d - 26a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24c x \|a \|c
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 453
+
+--S 454 of 1000
+--m0:=a0-r0
+--E 454
+
+--S 455 of 1000
+--d0:=D(m0,x)
+--E 455
+
+)clear all
+
+--S 456 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^5
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R -----------------------------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 1000
+r0:=-1/24*(5*b*c+3*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x^3)-_
+ 1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^4+1/64*(5*b^4*c^4-60*a*b^3*c^3*d-_
+ 90*a^2*b^2*c^2*d^2+20*a^3*b*c*d^3-3*a^4*d^4)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))+2*b^(5/2)*_
+ d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-_
+ 1/32*(5*b*c-a*d)*(b*c+3*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c^2*x^2)-_
+ 1/64*(5*b^3*c^3+73*a*b^2*c^2*d-17*a^2*b*c*d^2+3*a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 4 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 384a b c d x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 9a d + 60a b c d - 270a b c d - 180a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (9a d - 57a b c d - 337a b c d - 15b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 6a c d - 244a b c d - 118a b c )x + (- 72a c d - 136a b c )x
+--R +
+--R 3 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 1000
+--m0:=a0-r0
+--E 459
+
+--S 460 of 1000
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^6
+--R
+--R
+--R (1)
+--R 2 3 2 2 2 2 +-------+ +-------+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R -----------------------------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 1000
+r0:=-1/8*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c^2*x^4)-_
+ 1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(c*x^5)-3/128*(b*c-a*d)^5*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))-_
+ 1/64*(b*c-a*d)^3*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^3*x^2)-_
+ 1/16*(b*c-a*d)^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^3*x^3)+_
+ 3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (15a d - 75a b c d + 150a b c d - 150a b c d + 75a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 15a d + 70a b c d - 128a b c d - 70a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (10a c d - 46a b c d - 466a b c d - 10a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2 4 3 3 4
+--R (- 8a c d - 512a b c d - 248a b c )x + (- 176a c d - 336a b c )x
+--R +
+--R 4 4
+--R - 128a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 3 5 +-+ +-+
+--R 640a c x \|a \|c
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1000
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 1000
+--m0:=a0-r0
+--E 464
+
+--S 465 of 1000
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 1000
+t0:=x*(a+b*x)^(5/2)*(c+d*x)^(5/2)
+--R
+--R
+--R (1)
+--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 466
+
+--S 467 of 1000
+r0:=-1/24*(b*c-a*d)*(b*c+a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^3*d)-_
+ 1/12*(b*c+a*d)*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b^2*d)+_
+ 1/7*(a+b*x)^(7/2)*(c+d*x)^(7/2)/(b*d)+5/1024*(b*c-a*d)^6*_
+ (b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(9/2)*d^(9/2))+5/1536*(b*c-a*d)^4*(b*c+a*d)*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(b^4*d^3)-1/384*(b*c-a*d)^3*(b*c+a*d)*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b^4*d^2)-1/64*(b*c-a*d)^2*(b*c+a*d)*(a+b*x)^(7/2)*_
+ sqrt(c+d*x)/(b^4*d)-5/1024*(b*c-a*d)^5*(b*c+a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^4*d^4)
+--R
+--R
+--R (2)
+--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3
+--R 105a d - 525a b c d + 945a b c d - 525a b c d - 525a b c d
+--R +
+--R 2 5 5 2 6 6 7 7
+--R 945a b c d - 525a b c d + 105b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 6 6 6 5 6 6 5 5
+--R 3072b d x + (7424a b d + 7424b c d )x
+--R +
+--R 2 4 6 5 5 6 2 4 4
+--R (4736a b d + 18688a b c d + 4736b c d )x
+--R +
+--R 3 3 6 2 4 5 5 2 4 6 3 3 3
+--R (48a b d + 12752a b c d + 12752a b c d + 48b c d )x
+--R +
+--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2
+--R (- 56a b d + 256a b c d + 9840a b c d + 256a b c d - 56b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R 70a b d - 322a b c d + 508a b c d + 508a b c d - 322a b c d
+--R +
+--R 6 5
+--R 70b c d
+--R *
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 105a d + 490a b c d - 791a b c d + 300a b c d - 791a b c d
+--R +
+--R 5 5 6 6
+--R 490a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 4 +-+ +-+
+--R 21504b d \|b \|d
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 1000
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 1000
+--m0:=a0-r0
+--E 469
+
+--S 470 of 1000
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)
+--R
+--R
+--R (1)
+--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 471
+
+--S 472 of 1000
+r0:=1/12*(b*c-a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/b^2+1/6*(a+b*x)^(7/2)*_
+ (c+d*x)^(5/2)/b-5/512*(b*c-a*d)^6*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-5/768*(b*c-a*d)^4*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)+1/192*(b*c-a*d)^3*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b^3*d)+1/32*(b*c-a*d)^2*(a+b*x)^(7/2)*sqrt(c+d*x)/b^3+_
+ 5/512*(b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 15a d + 90a b c d - 225a b c d + 300a b c d - 225a b c d
+--R +
+--R 5 5 6 6
+--R 90a b c d - 15b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 5 5 4 5 5 4 4
+--R 256b d x + (640a b d + 640b c d )x
+--R +
+--R 2 3 5 4 4 5 2 3 3
+--R (432a b d + 1696a b c d + 432b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5 3 2 2
+--R (8a b d + 1272a b c d + 1272a b c d + 8b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4
+--R (- 10a b d + 56a b c d + 1188a b c d + 56a b c d - 10b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R 15a d - 85a b c d + 198a b c d + 198a b c d - 85a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 1536b d \|b \|d
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1000
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 1000
+--m0:=a0-r0
+--E 474
+
+--S 475 of 1000
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x
+--R
+--R
+--R (1)
+--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 /
+--R x
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 1000
+r0:=1/8*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/d+1/5*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)-2*a^(5/2)*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))+1/128*(b*c+a*d)*(3*b^4*c^4-28*a*b^3*c^3*d+_
+ 178*a^2*b^2*c^2*d^2-28*a^3*b*c*d^3+3*a^4*d^4)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))+_
+ 1/192*(3*b^3*c^3-19*a*b^2*c^2*d+109*a^2*b*c*d^2+3*a^3*d^3)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/(b*d^2)-1/48*(3*b^2*c^2-16*a*b*c*d-_
+ 3*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/d^2+1/128*(3*b^4*c^4-_
+ 22*a*b^3*c^3*d+128*a^2*b^2*c^2*d^2+22*a^3*b*c*d^3-3*a^4*d^4)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 45a d - 375a b c d + 2250a b c d + 2250a b c d - 375a b c d
+--R +
+--R 5 5
+--R 45b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R - 3840a b c d \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 384b d x + (1008a b d + 1008b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (744a b d + 2896a b c d + 744b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (30a b d + 2578a b c d + 2578a b c d + 30b c d)x - 45a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R 360a b c d + 3754a b c d + 360a b c d - 45b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 1920b d \|b \|d
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 1000
+--m0:=a0-r0
+--E 479
+
+--S 480 of 1000
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^2
+--R
+--R
+--R (1)
+--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 /
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 1000
+r0:=5/4*b*(a+b*x)^(3/2)*(c+d*x)^(5/2)-(a+b*x)^(5/2)*(c+d*x)^(5/2)/x-_
+ 5*a^(3/2)*c^(3/2)*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))-5/64*(b^4*c^4-20*a*b^3*c^3*d-_
+ 90*a^2*b^2*c^2*d^2-20*a^3*b*c*d^3+a^4*d^4)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))-5/96*_
+ (b^2*c^2-18*a*b*c*d-31*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/d+_
+ 5/24*b*(b*c+7*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/d-5/64*(b^3*c^3-_
+ 19*a*b^2*c^2*d-45*a^2*b*c*d^2-a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d + 300a b c d + 1350a b c d + 300a b c d - 15b c )x
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R (- 960a b c d - 960a b c d)x\|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 4 2 3 3 2 3
+--R 48b d x + (136a b d + 136b c d )x
+--R +
+--R 2 3 2 2 3 2 2
+--R (118a b d + 452a b c d + 118b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2
+--R (15a d + 601a b c d + 601a b c d + 15b c )x - 192a b c d
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R 192b d x\|b \|d
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 1000
+--m0:=a0-r0
+--E 484
+
+--S 485 of 1000
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^3
+--R
+--R
+--R (1)
+--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 /
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1000
+r0:=-5/4*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x)-1/2*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)/x^2-5/4*(3*b*c+a*d)*(b*c+3*a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+5/8*(b*c+a*d)*_
+ (b^2*c^2+14*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(sqrt(b)*sqrt(d))+5/12*(b^2*c^2+8*a*b*c*d+3*a^2*d^2)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/c+5/12*b*(5*b*c+3*a*d)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/c+5/8*(b^2*c^2+10*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 2 \|d \|b x + a
+--R (15a d + 225a b c d + 225a b c d + 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a
+--R (- 90a d - 300a b c d - 90b c )x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R 8b d x + (26a b d + 26b c d)x + (33a d + 122a b c d + 33b c )x
+--R +
+--R 2 2 2 2
+--R (- 54a c d - 54a b c )x - 12a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 24x \|b \|d
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 1000
+--m0:=a0-r0
+--E 489
+
+--S 490 of 1000
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^4
+--R
+--R
+--R (1)
+--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 /
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 1000
+r0:=-5/12*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^2)-1/3*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)/x^3-5/8*(b*c+a*d)*(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)))/(sqrt(a)*sqrt(c))+_
+ 5/4*(3*b*c+a*d)*(b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))*sqrt(b)*sqrt(d)+5/24*d*(9*b^2*c^2+14*a*b*c*d+a^2*d^2)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/c^2-5/24*(3*b^2*c^2+12*a*b*c*d+a^2*d^2)*_
+ (c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x)+5/8*d*(5*b^2*c^2+10*a*b*c*d+_
+ a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/c
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 3 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R (90a d + 300a b c d + 90b c )x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 15a d - 225a b c d - 225a b c d - 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 4 2 2 3
+--R 12b d x + (54a b d + 54b c d)x
+--R +
+--R 2 2 2 2 2 2 2 2 2
+--R (- 33a d - 122a b c d - 33b c )x + (- 26a c d - 26a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24x \|a \|c
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 1000
+--m0:=a0-r0
+--E 494
+
+--S 495 of 1000
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^5
+--R
+--R
+--R (1)
+--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 /
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1000
+r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^3)-1/4*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)/x^4+5/64*(b^4*c^4-20*a*b^3*c^3*d-90*a^2*b^2*c^2*d^2-_
+ 20*a^3*b*c*d^3+a^4*d^4)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(3/2)*c^(3/2))+5*b^(3/2)*d^(3/2)*(b*c+a*d)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-5/192*(3*b*c+a*d)*_
+ (b^2*c^2+24*a*b*c*d-a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x)-_
+ 5/96*(3*b^2*c^2+14*a*b*c*d-a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/_
+ (c^2*x^2)+5/64*d*(b^3*c^3+45*a*b^2*c^2*d+19*a^2*b*c*d^2-a^3*d^3)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 4 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R (960a b c d + 960a b c d)x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d - 300a b c d - 1350a b c d - 300a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 4 3 3 2 2 2 2 3 3 3
+--R 192a b c d x + (- 15a d - 601a b c d - 601a b c d - 15b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 118a c d - 452a b c d - 118a b c )x + (- 136a c d - 136a b c )x
+--R +
+--R 3 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 1000
+--m0:=a0-r0
+--E 499
+
+--S 500 of 1000
+--d0:=D(m0,x)
+--E 500
+
+)clear all
+
+--S 501 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^6
+--R
+--R
+--R (1)
+--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 /
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1000
+r0:=-1/8*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^4)-1/5*(a+b*x)^(5/2)*_
+ (c+d*x)^(5/2)/x^5-1/128*(b*c+a*d)*(3*b^4*c^4-28*a*b^3*c^3*d+_
+ 178*a^2*b^2*c^2*d^2-28*a^3*b*c*d^3+3*a^4*d^4)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+2*b^(5/2)*_
+ d^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-_
+ 1/192*(3*b^3*c^3+109*a*b^2*c^2*d-19*a^2*b*c*d^2+3*a^3*d^3)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x^2)-1/48*(3*b^2*c^2+16*a*b*c*d-_
+ 3*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x^3)+1/128*(3*b^4*c^4-_
+ 22*a*b^3*c^3*d-128*a^2*b^2*c^2*d^2+22*a^3*b*c*d^3-3*a^4*d^4)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 5 +-+ +-+ +-+ +-+ \|d \|b x + a
+--R 3840a b c d x \|a \|b \|c \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 45a d + 375a b c d - 2250a b c d - 2250a b c d + 375a b c d
+--R +
+--R 5 5
+--R - 45b c
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (45a d - 360a b c d - 3754a b c d - 360a b c d + 45b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (- 30a c d - 2578a b c d - 2578a b c d - 30a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2
+--R (- 744a c d - 2896a b c d - 744a b c )x
+--R +
+--R 4 3 3 4 4 4
+--R (- 1008a c d - 1008a b c )x - 384a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 5 +-+ +-+
+--R 1920a c x \|a \|c
+--R Type: Expression(Integer)
+--E 502
+
+--S 503 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 503
+
+--S 504 of 1000
+--m0:=a0-r0
+--E 504
+
+--S 505 of 1000
+--d0:=D(m0,x)
+--E 505
+
+)clear all
+
+--S 506 of 1000
+t0:=(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^7
+--R
+--R
+--R (1)
+--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 /
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1000
+r0:=-1/12*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(c^2*x^5)-_
+ 1/6*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(c*x^6)+5/512*(b*c-a*d)^6*_
+ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))+_
+ 5/768*(b*c-a*d)^4*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c^3*x^2)-_
+ 1/192*(b*c-a*d)^3*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c^3*x^3)-_
+ 1/32*(b*c-a*d)^2*(c+d*x)^(7/2)*sqrt(a+b*x)/(c^3*x^4)-_
+ 5/512*(b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x)
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 15a d - 90a b c d + 225a b c d - 300a b c d + 225a b c d
+--R +
+--R 5 5 6 6
+--R - 90a b c d + 15b c
+--R *
+--R +-+ +-------+
+--R 6 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 15a d + 85a b c d - 198a b c d - 198a b c d + 85a b c d
+--R +
+--R 5 5
+--R - 15b c
+--R *
+--R 5
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 4
+--R (10a c d - 56a b c d - 1188a b c d - 56a b c d + 10a b c )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 3
+--R (- 8a c d - 1272a b c d - 1272a b c d - 8a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5 2 5 4 4 5
+--R (- 432a c d - 1696a b c d - 432a b c )x + (- 640a c d - 640a b c )x
+--R +
+--R 5 5
+--R - 256a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 3 6 +-+ +-+
+--R 1536a c x \|a \|c
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 1000
+--a0:=integrate(t0,x)
+--E 508
+
+--S 509 of 1000
+--m0:=a0-r0
+--E 509
+
+--S 510 of 1000
+--d0:=D(m0,x)
+--E 510
+
+)clear all
+
+--S 511 of 1000
+t0:=x^2*(a+b*x)^(5/2)/sqrt(c+d*x)
+--R
+--R
+--R 2 4 3 2 2 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R (1) ---------------------------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1000
+r0:=-1/128*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(11/2))-_
+ 1/192*(b*c-a*d)*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(b^2*d^4)+1/240*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*_
+ (a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d^3)-3/40*(3*b*c+a*d)*(a+b*x)^(7/2)*_
+ sqrt(c+d*x)/(b^2*d^2)+1/5*x*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d)+_
+ 1/128*(b*c-a*d)^2*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^2*d^5)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 45a d + 75a b c d + 450a b c d - 2250a b c d + 2625a b c d
+--R +
+--R 5 5
+--R - 945b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 384b d x + (1008a b d - 432b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (744a b d - 1184a b c d + 504b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (30a b d - 962a b c d + 1498a b c d - 630b c d)x - 45a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 90a b c d + 1564a b c d - 2310a b c d + 945b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 5 +-+ +-+
+--R 1920b d \|b \|d
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 1000
+--a0:=integrate(t0,x)
+--E 513
+
+--S 514 of 1000
+--m0:=a0-r0
+--E 514
+
+--S 515 of 1000
+--d0:=D(m0,x)
+--E 515
+
+)clear all
+
+--S 516 of 1000
+t0:=x*(a+b*x)^(5/2)/sqrt(c+d*x)
+--R
+--R
+--R 2 3 2 2 +-------+
+--R (b x + 2a b x + a x)\|b x + a
+--R (1) --------------------------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1000
+r0:=5/64*(b*c-a*d)^3*(7*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(3/2)*d^(9/2))+5/96*(b*c-a*d)*(7*b*c+a*d)*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^3)-1/24*(7*b*c+a*d)*(a+b*x)^(5/2)*_
+ sqrt(c+d*x)/(b*d^2)+1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d)-_
+ 5/64*(b*c-a*d)^2*(7*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d - 60a b c d + 270a b c d - 300a b c d + 105b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (136a b d - 56b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2
+--R (118a b d - 172a b c d + 70b c d)x + 15a d - 191a b c d
+--R +
+--R 2 2 3 3
+--R 265a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1000
+--a0:=integrate(t0,x)
+--E 518
+
+--S 519 of 1000
+--m0:=a0-r0
+--E 519
+
+--S 520 of 1000
+--d0:=D(m0,x)
+--E 520
+
+)clear all
+
+--S 521 of 1000
+t0:=(a+b*x)^(5/2)/sqrt(c+d*x)
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1000
+r0:=-5/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (d^(7/2)*sqrt(b))-5/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^2+_
+ 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/d+5/8*(b*c-a*d)^2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/d^3
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (15a d - 45a b c d + 45a b c d - 15b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (26a b d - 10b c d)x + 33a d - 40a b c d + 15b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24d \|b \|d
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1000
+--a0:=integrate(t0,x)
+--E 523
+
+--S 524 of 1000
+--m0:=a0-r0
+--E 524
+
+--S 525 of 1000
+--d0:=D(m0,x)
+--E 525
+
+)clear all
+
+--S 526 of 1000
+t0:=(a+b*x)^(5/2)/(x*sqrt(c+d*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R +-------+
+--R x\|d x + c
+--R Type: Expression(Integer)
+--E 526
+
+--S 527 of 1000
+r0:=1/4*(3*b^2*c^2-10*a*b*c*d+15*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(5/2)-2*a^(5/2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(c)+1/2*b*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/d-1/4*b*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-+ \|d \|b x + a
+--R (15a d - 10a b c d + 3b c )\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|c \|b x + a
+--R - 8a d \|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+ +-------+
+--R (2b d x + 9a b d - 3b c)\|c \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4d \|c \|d
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 528
+
+--S 529 of 1000
+--m0:=a0-r0
+--E 529
+
+--S 530 of 1000
+--d0:=D(m0,x)
+--E 530
+
+)clear all
+
+--S 531 of 1000
+t0:=(a+b*x)^(5/2)/(x^2*sqrt(c+d*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 2 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 1000
+r0:=-a^(3/2)*(5*b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/c^(3/2)-b^(3/2)*(b*c-5*a*d)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(3/2)+b*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/c-(a+b*x)^(5/2)*sqrt(c+d*x)/(c*x)+b*(b*c+a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(c*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|d \|b x + a
+--R (5a b c d - b c )x\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|c \|b x + a
+--R (a d - 5a b c d)x\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+ +-------+
+--R (b c x - a d)\|c \|d \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R c d x\|c \|d
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 533
+
+--S 534 of 1000
+--m0:=a0-r0
+--E 534
+
+--S 535 of 1000
+--d0:=D(m0,x)
+--E 535
+
+)clear all
+
+--S 536 of 1000
+t0:=(a+b*x)^(5/2)/(x^3*sqrt(c+d*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 3 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1000
+r0:=-1/4*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(5/2)+2*b^(5/2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(d)-1/4*(5*b*c-3*a*d)*_
+ (a+b*x)^(3/2)*sqrt(c+d*x)/(c^2*x)-1/2*(a+b*x)^(5/2)*sqrt(c+d*x)/_
+ (c*x^2)+1/4*b*(7*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/c^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 +-+ +-+ \|d \|b x + a
+--R 8b c x \|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a
+--R (- 3a d + 10a b c d - 15b c )x \|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+ +-------+
+--R ((3a d - 9a b c)x - 2a c)\|c \|d \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4c x \|c \|d
+--R Type: Expression(Integer)
+--E 537
+
+--S 538 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 538
+
+--S 539 of 1000
+--m0:=a0-r0
+--E 539
+
+--S 540 of 1000
+--d0:=D(m0,x)
+--E 540
+
+)clear all
+
+--S 541 of 1000
+t0:=(a+b*x)^(5/2)/(x^4*sqrt(c+d*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 4 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1000
+r0:=-5/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (c^(7/2)*sqrt(a))-5/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(c^2*x^2)-_
+ 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(c*x^3)-5/8*(b*c-a*d)^2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(c^3*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (15a d - 45a b c d + 45a b c d - 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((- 15a d + 40a b c d - 33b c )x + (10a c d - 26a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 24c x \|a \|c
+--R Type: Expression(Integer)
+--E 542
+
+--S 543 of 1000
+--a0:=integrate(t0,x)
+--E 543
+
+--S 544 of 1000
+--m0:=a0-r0
+--E 544
+
+--S 545 of 1000
+--d0:=D(m0,x)
+--E 545
+
+)clear all
+
+--S 546 of 1000
+t0:=(a+b*x)^(5/2)/(x^5*sqrt(c+d*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 5 +-------+
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1000
+r0:=5/64*(b*c-a*d)^3*(b*c+7*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(3/2)*c^(9/2))-1/24*(5*b*c-7*a*d)*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(c^2*x^3)-1/4*(a+b*x)^(5/2)*sqrt(c+d*x)/(c*x^4)-_
+ 1/96*(15*b^2*c^2-58*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_
+ (c^3*x^2)-1/192*(15*b^3*c^3-191*a*b^2*c^2*d+265*a^2*b*c*d^2-_
+ 105*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^4*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 105a d + 300a b c d - 270a b c d + 60a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (105a d - 265a b c d + 191a b c d - 15b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 70a c d + 172a b c d - 118a b c )x + (56a c d - 136a b c )x
+--R +
+--R 3 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 4 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 547
+
+--S 548 of 1000
+--a0:=integrate(t0,x)
+--E 548
+
+--S 549 of 1000
+--m0:=a0-r0
+--E 549
+
+--S 550 of 1000
+--d0:=D(m0,x)
+--E 550
+
+)clear all
+
+--S 551 of 1000
+t0:=x^2*(a+b*x)^(5/2)/(c+d*x)^(3/2)
+--R
+--R
+--R 2 4 3 2 2 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R (1) ---------------------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1000
+r0:=5/64*(b*c-a*d)^2*(63*b^2*c^2-14*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(11/2))+2*c^2*_
+ (a+b*x)^(7/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+5/96*(63*b^2*c^2-_
+ 14*a*b*c*d-a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^4)+_
+ 1/24*(14*a*c-63*b*c^2/d+a^2*d/b)*(a+b*x)^(5/2)*sqrt(c+d*x)/_
+ (d^2*(b*c-a*d))+1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d^2)-_
+ 5/64*(b*c-a*d)*(63*b^2*c^2-14*a*b*c*d-a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b*d^5)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d - 180a b c d + 1350a b c d - 2100a b c d + 945b c )
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 4 4 2 4 3 3 3
+--R 48b d x + (136a b d - 72b c d )x
+--R +
+--R 2 4 2 3 3 2 2 2
+--R (118a b d - 244a b c d + 126b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3 3
+--R (15a d - 337a b c d + 637a b c d - 315b c d)x + 15a c d
+--R +
+--R 2 2 2 2 3 3 4
+--R - 839a b c d + 1785a b c d - 945b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 5 +-+ +-+ +-------+
+--R 192b d \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 552
+
+--S 553 of 1000
+--a0:=integrate(t0,x)
+--E 553
+
+--S 554 of 1000
+--m0:=a0-r0
+--E 554
+
+--S 555 of 1000
+--d0:=D(m0,x)
+--E 555
+
+)clear all
+
+--S 556 of 1000
+t0:=x*(a+b*x)^(5/2)/(c+d*x)^(3/2)
+--R
+--R
+--R 2 3 2 2 +-------+
+--R (b x + 2a b x + a x)\|b x + a
+--R (1) --------------------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1000
+r0:=-5/8*(b*c-a*d)^2*(7*b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(d^(9/2)*sqrt(b))-2*c*(a+b*x)^(7/2)/(d*(b*c-a*d)*_
+ sqrt(c+d*x))-5/12*(7*b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3+_
+ 1/3*(7*b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(d^2*(b*c-a*d))+_
+ 5/8*(b*c-a*d)*(7*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^4
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-------+
+--R (15a d - 135a b c d + 225a b c d - 105b c )\|d x + c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 3 3 3 2 2 2 2 3 2 2 2
+--R 8b d x + (26a b d - 14b c d )x + (33a d - 68a b c d + 35b c d)x
+--R +
+--R 2 2 2 2 3
+--R 81a c d - 190a b c d + 105b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 4 +-+ +-+ +-------+
+--R 24d \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 557
+
+--S 558 of 1000
+--a0:=integrate(t0,x)
+--E 558
+
+--S 559 of 1000
+--m0:=a0-r0
+--E 559
+
+--S 560 of 1000
+--d0:=D(m0,x)
+--E 560
+
+)clear all
+
+--S 561 of 1000
+t0:=(a+b*x)^(5/2)/(c+d*x)^(3/2)
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R +-------+
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1000
+r0:=15/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(b)/d^(7/2)-2*(a+b*x)^(5/2)/(d*sqrt(c+d*x))+5/2*b*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/d^2-15/4*b*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^3
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-------+ \|d \|b x + a
+--R (15a d - 30a b c d + 15b c )\|b \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-------+
+--R (2b d x + (9a b d - 5b c d)x - 8a d + 25a b c d - 15b c )\|d \|b x + a
+--R /
+--R 3 +-+ +-------+
+--R 4d \|d \|d x + c
+--R Type: Expression(Integer)
+--E 562
+
+--S 563 of 1000
+--a0:=integrate(t0,x)
+--E 563
+
+--S 564 of 1000
+--m0:=a0-r0
+--E 564
+
+--S 565 of 1000
+--d0:=D(m0,x)
+--E 565
+
+)clear all
+
+--S 566 of 1000
+t0:=(a+b*x)^(5/2)/(x*(c+d*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 2 +-------+
+--R (d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1000
+r0:=-2*a^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(3/2)-_
+ b^(3/2)*(3*b*c-5*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ d^(5/2)+2*(a+b*x)^(5/2)/(c*sqrt(c+d*x))-2*b*(a+b*x)^(3/2)*_
+ sqrt(c+d*x)/(c*d)+b*(3*b*c-2*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*d^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|d \|b x + a
+--R (5a b c d - 3b c )\|b \|c \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|c \|b x + a
+--R - 2a d \|a \|d \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 +-+ +-+ +-------+
+--R (b c d x + 2a d - 4a b c d + 3b c )\|c \|d \|b x + a
+--R /
+--R 2 +-+ +-+ +-------+
+--R c d \|c \|d \|d x + c
+--R Type: Expression(Integer)
+--E 567
+
+--S 568 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 568
+
+--S 569 of 1000
+--m0:=a0-r0
+--E 569
+
+--S 570 of 1000
+--d0:=D(m0,x)
+--E 570
+
+)clear all
+
+--S 571 of 1000
+t0:=(a+b*x)^(5/2)/(x^2*(c+d*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 3 2 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1000
+r0:=-a^(3/2)*(5*b*c-3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ c^(5/2)+2*b^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ d^(3/2)+3*(b*c-a*d)*(a+b*x)^(3/2)/(c^2*sqrt(c+d*x))-(a+b*x)^(5/2)/_
+ (c*x*sqrt(c+d*x))-b*(2*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|d \|b x + a
+--R 2b c x\|b \|c \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|c \|b x + a
+--R (3a d - 5a b c d)x\|a \|d \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 +-+ +-+ +-------+
+--R ((- 3a d + 4a b c d - 2b c )x - a c d)\|c \|d \|b x + a
+--R /
+--R 2 +-+ +-+ +-------+
+--R c d x\|c \|d \|d x + c
+--R Type: Expression(Integer)
+--E 572
+
+--S 573 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 573
+
+--S 574 of 1000
+--m0:=a0-r0
+--E 574
+
+--S 575 of 1000
+--d0:=D(m0,x)
+--E 575
+
+)clear all
+
+--S 576 of 1000
+t0:=(a+b*x)^(5/2)/(x^3*(c+d*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 4 3 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 576
+
+--S 577 of 1000
+r0:=-15/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(a)/c^(7/2)-5/4*(b*c-a*d)*(a+b*x)^(3/2)/(c^2*x*sqrt(c+d*x))-_
+ 1/2*(a+b*x)^(5/2)/(c*x^2*sqrt(c+d*x))+15/4*(b*c-a*d)^2*_
+ sqrt(a+b*x)/(c^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-------+ \|c \|b x + a
+--R (- 15a d + 30a b c d - 15b c )x \|a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((15a d - 25a b c d + 8b c )x + (5a c d - 9a b c )x - 2a c )\|c
+--R *
+--R +-------+
+--R \|b x + a
+--R /
+--R 3 2 +-+ +-------+
+--R 4c x \|c \|d x + c
+--R Type: Expression(Integer)
+--E 577
+
+--S 578 of 1000
+--a0:=integrate(t0,x)
+--E 578
+
+--S 579 of 1000
+--m0:=a0-r0
+--E 579
+
+--S 580 of 1000
+--d0:=D(m0,x)
+--E 580
+
+)clear all
+
+--S 581 of 1000
+t0:=(a+b*x)^(5/2)/(x^4*(c+d*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 5 4 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 581
+
+--S 582 of 1000
+r0:=-5/8*(b*c-7*a*d)*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(c^(9/2)*sqrt(a))-1/12*(5*b*c-7*a*d)*(a+b*x)^(3/2)/_
+ (c^2*x^2*sqrt(c+d*x))-1/3*(a+b*x)^(5/2)/(c*x^3*sqrt(c+d*x))-_
+ 1/24*d*(81*b^2*c^2-190*a*b*c*d+105*a^2*d^2)*sqrt(a+b*x)/_
+ (c^4*sqrt(c+d*x))-1/24*(15*b^2*c^2-54*a*b*c*d+35*a^2*d^2)*_
+ sqrt(a+b*x)/(c^3*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 3 +-------+
+--R (105a d - 225a b c d + 135a b c d - 15b c )x \|d x + c
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 3
+--R (- 105a d + 190a b c d - 81b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3 2 3
+--R (- 35a c d + 68a b c d - 33b c )x + (14a c d - 26a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 4 3 +-+ +-+ +-------+
+--R 24c x \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 582
+
+--S 583 of 1000
+--a0:=integrate(t0,x)
+--E 583
+
+--S 584 of 1000
+--m0:=a0-r0
+--E 584
+
+--S 585 of 1000
+--d0:=D(m0,x)
+--E 585
+
+)clear all
+
+--S 586 of 1000
+t0:=(a+b*x)^(5/2)/(x^5*(c+d*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 6 5 +-------+
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 586
+
+--S 587 of 1000
+r0:=5/64*(b*c-a*d)^2*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(11/2))-_
+ 1/24*(5*b*c-9*a*d)*(a+b*x)^(3/2)/(c^2*x^3*sqrt(c+d*x))-_
+ 1/4*(a+b*x)^(5/2)/(c*x^4*sqrt(c+d*x))-1/192*d*(15*b^3*c^3-_
+ 839*a*b^2*c^2*d+1785*a^2*b*c*d^2-945*a^3*d^3)*sqrt(a+b*x)/_
+ (a*c^5*sqrt(c+d*x))-1/96*(15*b^2*c^2-86*a*b*c*d+63*a^2*d^2)*_
+ sqrt(a+b*x)/(c^3*x^2*sqrt(c+d*x))-1/192*(b*c-a*d)*(15*b^2*c^2-_
+ 322*a*b*c*d+315*a^2*d^2)*sqrt(a+b*x)/(a*c^4*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 945a d + 2100a b c d - 1350a b c d + 180a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (945a d - 1785a b c d + 839a b c d - 15b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 3
+--R (315a c d - 637a b c d + 337a b c d - 15b c )x
+--R +
+--R 3 2 2 2 3 2 4 2 3 3 2 4
+--R (- 126a c d + 244a b c d - 118a b c )x + (72a c d - 136a b c )x
+--R +
+--R 3 4
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 5 4 +-+ +-+ +-------+
+--R 192a c x \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 1000
+--a0:=integrate(t0,x)
+--E 588
+
+--S 589 of 1000
+--m0:=a0-r0
+--E 589
+
+--S 590 of 1000
+--d0:=D(m0,x)
+--E 590
+
+)clear all
+
+--S 591 of 1000
+t0:=x^3*(a+b*x)^(5/2)/(c+d*x)^(5/2)
+--R
+--R
+--R 2 5 4 2 3 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R (1) ---------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 1000
+r0:=-2/3*x^3*(a+b*x)^(5/2)/(d*(c+d*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(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(13/2))-2/3*(11*b*c-6*a*d)*_
+ x^2*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+5/96*(231*b^3*c^3-_
+ 189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (b*d^5*(b*c-a*d))-1/24*(231*b^2*c^2-156*a*b*c*d+5*a^2*d^2)*_
+ (a+b*x)^(5/2)*sqrt(c+d*x)/(b*d^4*(b*c-a*d))+1/12*(99*b*c-59*a*d)*_
+ x*(a+b*x)^(5/2)*sqrt(c+d*x)/(d^3*(b*c-a*d))-5/64*(231*b^3*c^3-_
+ 189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^6)
+--R
+--R
+--R (2)
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R (- 15a d - 300a b c d + 3150a b c d - 6300a b c d + 3465b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 15a c d - 300a b c d + 3150a b c d - 6300a b c d + 3465b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 5 5 2 5 3 4 4
+--R 48b d x + (136a b d - 88b c d )x
+--R +
+--R 2 5 2 4 3 2 3 3
+--R (118a b d - 316a b c d + 198b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 2
+--R (15a d - 483a b c d + 1161a b c d - 693b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 3 2 3
+--R (30a c d - 2472a b c d + 7014a b c d - 4620b c d)x + 15a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 1743a b c d + 5145a b c d - 3465b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 7 6 +-+ +-+ +-------+
+--R (192b d x + 192b c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1000
+--a0:=integrate(t0,x)
+--E 593
+
+--S 594 of 1000
+--m0:=a0-r0
+--E 594
+
+--S 595 of 1000
+--d0:=D(m0,x)
+--E 595
+
+)clear all
+
+--S 596 of 1000
+t0:=x^2*(a+b*x)^(5/2)/(c+d*x)^(5/2)
+--R
+--R
+--R 2 4 3 2 2 +-------+
+--R (b x + 2a b x + a x )\|b x + a
+--R (1) ---------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1000
+r0:=2/3*c^2*(a+b*x)^(7/2)/(d^2*(b*c-a*d)*(c+d*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(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(d^(11/2)*sqrt(b))-4/3*c*(5*b*c-3*a*d)*_
+ (a+b*x)^(7/2)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))-5/12*(21*b^2*c^2-_
+ 14*a*b*c*d+a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(d^4*(b*c-a*d))+_
+ 1/3*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/_
+ (d^3*(b*c-a*d)^2)+5/8*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/d^5
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 3 3
+--R (15a d - 225a b c d + 525a b c d - 315b c d)x + 15a c d
+--R +
+--R 2 2 2 2 3 3 4
+--R - 225a b c d + 525a b c d - 315b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 4 4 4 2 3 3
+--R 8b d x + (26a b d - 18b c d )x
+--R +
+--R 2 4 3 2 2 2 2
+--R (33a d - 96a b c d + 63b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 3
+--R (162a c d - 574a b c d + 420b c d)x + 113a c d - 420a b c d
+--R +
+--R 2 4
+--R 315b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 6 5 +-+ +-+ +-------+
+--R (24d x + 24c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 597
+
+--S 598 of 1000
+--a0:=integrate(t0,x)
+--E 598
+
+--S 599 of 1000
+--m0:=a0-r0
+--E 599
+
+--S 600 of 1000
+--d0:=D(m0,x)
+--E 600
+
+)clear all
+
+--S 601 of 1000
+t0:=x*(a+b*x)^(5/2)/(c+d*x)^(5/2)
+--R
+--R
+--R 2 3 2 2 +-------+
+--R (b x + 2a b x + a x)\|b x + a
+--R (1) --------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1000
+r0:=-2/3*c*(a+b*x)^(7/2)/(d*(b*c-a*d)*(c+d*x)^(3/2))+5/4*(7*b*c-3*a*d)*_
+ (b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(b)/d^(9/2)-2/3*(7*b*c-3*a*d)*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*_
+ sqrt(c+d*x))+5/6*b*(7*b*c-3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/_
+ (d^3*(b*c-a*d))-5/4*b*(7*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^4
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 3
+--R ((45a d - 150a b c d + 105b c d)x + 45a c d - 150a b c d + 105b c )
+--R *
+--R +-+ +-------+
+--R +-+ +-------+ \|d \|b x + a
+--R \|b \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 3 3 3 2 2 2
+--R 6b d x + (27a b d - 21b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2 3
+--R (- 24a d + 158a b c d - 140b c d)x - 16a c d + 115a b c d - 105b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R /
+--R 5 4 +-+ +-------+
+--R (12d x + 12c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 602
+
+--S 603 of 1000
+--a0:=integrate(t0,x)
+--E 603
+
+--S 604 of 1000
+--m0:=a0-r0
+--E 604
+
+--S 605 of 1000
+--d0:=D(m0,x)
+--E 605
+
+)clear all
+
+--S 606 of 1000
+t0:=(a+b*x)^(5/2)/(c+d*x)^(5/2)
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1000
+r0:=-2/3*(a+b*x)^(5/2)/(d*(c+d*x)^(3/2))-5*b^(3/2)*(b*c-a*d)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(7/2)-10/3*b*(a+b*x)^(3/2)/_
+ (d^2*sqrt(c+d*x))+5*b^2*sqrt(a+b*x)*sqrt(c+d*x)/d^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ +-------+
+--R ((15a b d - 15b c d)x + 15a b c d - 15b c )\|b \|d x + c
+--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 + (- 14a b d + 20b c d)x - 2a d - 10a b c d + 15b c )\|d
+--R *
+--R +-------+
+--R \|b x + a
+--R /
+--R 4 3 +-+ +-------+
+--R (3d x + 3c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 1000
+--a0:=integrate(t0,x)
+--E 608
+
+--S 609 of 1000
+--m0:=a0-r0
+--E 609
+
+--S 610 of 1000
+--d0:=D(m0,x)
+--E 610
+
+)clear all
+
+--S 611 of 1000
+t0:=(a+b*x)^(5/2)/(x*(c+d*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 2 3 2 2 +-------+
+--R (d x + 2c d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1000
+r0:=2/3*(a+b*x)^(5/2)/(c*(c+d*x)^(3/2))-2*a^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/c^(5/2)+2*b^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/d^(5/2)+2/3*(2*b*c+3*a*d)*(a+b*x)^(3/2)/_
+ (c^2*d*sqrt(c+d*x))-2*b*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*d^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 3 +-+ +-+ +-------+ \|d \|b x + a
+--R (6b c d x + 6b c )\|b \|c \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 3 2 2 +-+ +-+ +-------+ \|c \|b x + a
+--R (- 6a d x - 6a c d )\|a \|d \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 3 +-+ +-+
+--R ((6a d + 2a b c d - 8b c d)x + 8a c d - 2a b c d - 6b c )\|c \|d
+--R *
+--R +-------+
+--R \|b x + a
+--R /
+--R 2 3 3 2 +-+ +-+ +-------+
+--R (3c d x + 3c d )\|c \|d \|d x + c
+--R Type: Expression(Integer)
+--E 612
+
+--S 613 of 1000
+--a0:=integrate(t0,x)
+--E 613
+
+--S 614 of 1000
+--m0:=a0-r0
+--E 614
+
+--S 615 of 1000
+--d0:=D(m0,x)
+--E 615
+
+)clear all
+
+--S 616 of 1000
+t0:=(a+b*x)^(5/2)/(x^2*(c+d*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ---------------------------------
+--R 2 4 3 2 2 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1000
+r0:=5/3*(b*c-a*d)*(a+b*x)^(3/2)/(c^2*(c+d*x)^(3/2))-(a+b*x)^(5/2)/_
+ (c*x*(c+d*x)^(3/2))-5*a^(3/2)*(b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/c^(7/2)+5*a*(b*c-a*d)*sqrt(a+b*x)/(c^3*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 +-+ +-------+
+--R ((15a d - 15a b c d)x + (15a c d - 15a b c )x)\|a \|d x + c
+--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 ((- 15a d + 10a b c d + 2b c )x + (- 20a c d + 14a b c )x - 3a c )
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R /
+--R 3 2 4 +-+ +-------+
+--R (3c d x + 3c x)\|c \|d x + c
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 1000
+--a0:=integrate(t0,x)
+--E 618
+
+--S 619 of 1000
+--m0:=a0-r0
+--E 619
+
+--S 620 of 1000
+--d0:=D(m0,x)
+--E 620
+
+)clear all
+
+--S 621 of 1000
+t0:=(a+b*x)^(5/2)/(x^3*(c+d*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ---------------------------------
+--R 2 5 4 2 3 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1000
+r0:=-1/4*(5*b*c-7*a*d)*(a+b*x)^(3/2)/(c^2*x*(c+d*x)^(3/2))-1/2*(a+b*x)^(5/2)/_
+ (c*x^2*(c+d*x)^(3/2))-5/4*(3*b*c-7*a*d)*(b*c-a*d)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(9/2)+1/12*(29*b*c-_
+ 35*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^3*(c+d*x)^(3/2))+1/12*(16*b^2*c^2-_
+ 115*a*b*c*d+105*a^2*d^2)*sqrt(a+b*x)/(c^4*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 3
+--R (- 105a d + 150a b c d - 45b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (- 105a c d + 150a b c d - 45b c )x
+--R *
+--R +-+ +-------+
+--R +-+ +-------+ \|c \|b x + a
+--R \|a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 3
+--R (105a d - 115a b c d + 16b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3 2 3
+--R (140a c d - 158a b c d + 24b c )x + (21a c d - 27a b c )x - 6a c
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R /
+--R 4 3 5 2 +-+ +-------+
+--R (12c d x + 12c x )\|c \|d x + c
+--R Type: Expression(Integer)
+--E 622
+
+--S 623 of 1000
+--a0:=integrate(t0,x)
+--E 623
+
+--S 624 of 1000
+--m0:=a0-r0
+--E 624
+
+--S 625 of 1000
+--d0:=D(m0,x)
+--E 625
+
+)clear all
+
+--S 626 of 1000
+t0:=(a+b*x)^(5/2)/(x^4*(c+d*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ---------------------------------
+--R 2 6 5 2 4 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1000
+r0:=-1/12*(5*b*c-9*a*d)*(a+b*x)^(3/2)/(c^2*x^2*(c+d*x)^(3/2))-_
+ 1/3*(a+b*x)^(5/2)/(c*x^3*(c+d*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(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(c^(11/2)*sqrt(a))-7/24*d*(7*b*c-15*a*d)*(b*c-a*d)*_
+ sqrt(a+b*x)/(c^4*(c+d*x)^(3/2))-1/8*(5*b*c-21*a*d)*(b*c-a*d)*_
+ sqrt(a+b*x)/(c^3*x*(c+d*x)^(3/2))-1/24*d*(113*b^2*c^2-_
+ 420*a*b*c*d+315*a^2*d^2)*sqrt(a+b*x)/(c^5*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 4
+--R (315a d - 525a b c d + 225a b c d - 15b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 3
+--R (315a c d - 525a b c d + 225a b c d - 15b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 315a d + 420a b c d - 113b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 420a c d + 574a b c d - 162b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4 2 4
+--R (- 63a c d + 96a b c d - 33b c )x + (18a c d - 26a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 5 4 6 3 +-+ +-+ +-------+
+--R (24c d x + 24c x )\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 627
+
+--S 628 of 1000
+--a0:=integrate(t0,x)
+--E 628
+
+--S 629 of 1000
+--m0:=a0-r0
+--E 629
+
+--S 630 of 1000
+--d0:=D(m0,x)
+--E 630
+
+)clear all
+
+--S 631 of 1000
+t0:=(a+b*x)^(5/2)/(x^5*(c+d*x)^(5/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (b x + 2a b x + a )\|b x + a
+--R (1) ---------------------------------
+--R 2 7 6 2 5 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1000
+r0:=-1/24*(5*b*c-11*a*d)*(a+b*x)^(3/2)/(c^2*x^3*(c+d*x)^(3/2))-_
+ 1/4*(a+b*x)^(5/2)/(c*x^4*(c+d*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(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(13/2))-1/64*_
+ d*(b*c-a*d)*(5*b^2*c^2-238*a*b*c*d+385*a^2*d^2)*sqrt(a+b*x)/_
+ (a*c^5*(c+d*x)^(3/2))-1/32*(5*b*c-33*a*d)*(b*c-a*d)*sqrt(a+b*x)/_
+ (c^3*x^2*(c+d*x)^(3/2))-1/64*(b*c-a*d)*(5*b^2*c^2-156*a*b*c*d+_
+ 231*a^2*d^2)*sqrt(a+b*x)/(a*c^4*x*(c+d*x)^(3/2))-1/64*d*(5*b^3*c^3-_
+ 581*a*b^2*c^2*d+1715*a^2*b*c*d^2-1155*a^3*d^3)*sqrt(a+b*x)/_
+ (a*c^6*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 5
+--R (- 3465a d + 6300a b c d - 3150a b c d + 300a b c d + 15b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4
+--R (- 3465a c d + 6300a b c d - 3150a b c d + 300a b c d + 15b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 5
+--R (3465a d - 5145a b c d + 1743a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (4620a c d - 7014a b c d + 2472a b c d - 30b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 3
+--R (693a c d - 1161a b c d + 483a b c d - 15b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (- 198a c d + 316a b c d - 118a b c )x + (88a c d - 136a b c )x
+--R +
+--R 3 5
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 6 5 7 4 +-+ +-+ +-------+
+--R (192a c d x + 192a c x )\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 632
+
+--S 633 of 1000
+--a0:=integrate(t0,x)
+--E 633
+
+--S 634 of 1000
+--m0:=a0-r0
+--E 634
+
+--S 635 of 1000
+--d0:=D(m0,x)
+--E 635
+
+)clear all
+
+--S 636 of 1000
+t0:=x^2*sqrt(c+d*x)/sqrt(a+b*x)
+--R
+--R
+--R 2 +-------+
+--R x \|d x + c
+--R (1) ------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1000
+r0:=1/8*(b*c-a*d)*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-1/12*(3*b*c+5*a*d)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/(b^2*d^2)+1/3*x*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(b*d)+1/8*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^3*d^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 15a d + 9a b c d + 3a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (- 10a b d + 2b c d)x + 15a d - 4a b c d - 3b c )\|b \|d
+--R *
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R /
+--R 3 2 +-+ +-+
+--R 24b d \|b \|d
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 1000
+--a0:=integrate(t0,x)
+--E 638
+
+--S 639 of 1000
+--m0:=a0-r0
+--E 639
+
+--S 640 of 1000
+--d0:=D(m0,x)
+--E 640
+
+)clear all
+
+--S 641 of 1000
+t0:=x*sqrt(c+d*x)/sqrt(a+b*x)
+--R
+--R
+--R +-------+
+--R x\|d x + c
+--R (1) -----------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1000
+r0:=-1/4*(b*c-a*d)*(b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(b*d)-_
+ 1/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d - 2a b c d - b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (2b d x - 3a d + b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4b d\|b \|d
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 1000
+--a0:=integrate(t0,x)
+--E 643
+
+--S 644 of 1000
+--m0:=a0-r0
+--E 644
+
+--S 645 of 1000
+--d0:=D(m0,x)
+--E 645
+
+)clear all
+
+--S 646 of 1000
+t0:=sqrt(c+d*x)/sqrt(a+b*x)
+--R
+--R
+--R +-------+
+--R \|d x + c
+--R (1) ----------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1000
+r0:=(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(3/2)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x)/b
+--R
+--R
+--R +-+ +-------+
+--R \|d \|b x + a +-+ +-+ +-------+ +-------+
+--R (- a d + b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|b \|d x + c
+--R (2) -----------------------------------------------------------------
+--R +-+ +-+
+--R b\|b \|d
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1000
+--a0:=integrate(t0,x)
+--E 648
+
+--S 649 of 1000
+--m0:=a0-r0
+--E 649
+
+--S 650 of 1000
+--d0:=D(m0,x)
+--E 650
+
+)clear all
+
+--S 651 of 1000
+t0:=sqrt(c+d*x)/(x*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R \|d x + c
+--R (1) -----------
+--R +-------+
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/sqrt(a)+_
+ 2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)
+--R
+--R
+--R +-+ +-------+ +-+ +-------+
+--R +-+ +-+ \|d \|b x + a +-+ +-+ \|c \|b x + a
+--R 2\|a \|d atanh(--------------) - 2\|b \|c atanh(--------------)
+--R +-+ +-------+ +-+ +-------+
+--R \|b \|d x + c \|a \|d x + c
+--R (2) ---------------------------------------------------------------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 652
+
+--S 653 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 653
+
+--S 654 of 1000
+--m0:=a0-r0
+--E 654
+
+--S 655 of 1000
+--d0:=D(m0,x)
+--E 655
+
+)clear all
+
+--S 656 of 1000
+t0:=sqrt(c+d*x)/(x^2*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R \|d x + c
+--R (1) ------------
+--R 2 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1000
+r0:=(b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(3/2)*sqrt(c))-sqrt(a+b*x)*sqrt(c+d*x)/(a*x)
+--R
+--R
+--R +-+ +-------+
+--R \|c \|b x + a +-+ +-+ +-------+ +-------+
+--R (- a d + b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|a \|d x + c
+--R (2) -------------------------------------------------------------------
+--R +-+ +-+
+--R a x\|a \|c
+--R Type: Expression(Integer)
+--E 657
+
+--S 658 of 1000
+--a0:=integrate(t0,x)
+--E 658
+
+--S 659 of 1000
+--m0:=a0-r0
+--E 659
+
+--S 660 of 1000
+--d0:=D(m0,x)
+--E 660
+
+)clear all
+
+--S 661 of 1000
+t0:=sqrt(c+d*x)/(x^3*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R \|d x + c
+--R (1) ------------
+--R 3 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1000
+r0:=-1/4*(b*c-a*d)*(3*b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(3/2))-1/2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a*x^2)+1/4*(3*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (a d + 2a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R ((- a d + 3b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4a c x \|a \|c
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1000
+--a0:=integrate(t0,x)
+--E 663
+
+--S 664 of 1000
+--m0:=a0-r0
+--E 664
+
+--S 665 of 1000
+--d0:=D(m0,x)
+--E 665
+
+)clear all
+
+--S 666 of 1000
+t0:=sqrt(c+d*x)/(x^4*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R \|d x + c
+--R (1) ------------
+--R 4 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1000
+r0:=1/8*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/3*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a*x^3)+1/12*(5*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/_
+ (a^2*c*x^2)-1/24*(5*b*c-3*a*d)*(3*b*c+a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^3*c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 3a d - 3a b c d - 9a b c d + 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((3a d + 4a b c d - 15b c )x + (- 2a c d + 10a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 3 2 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 667
+
+--S 668 of 1000
+--a0:=integrate(t0,x)
+--E 668
+
+--S 669 of 1000
+--m0:=a0-r0
+--E 669
+
+--S 670 of 1000
+--d0:=D(m0,x)
+--E 670
+
+)clear all
+
+--S 671 of 1000
+t0:=x^2*(c+d*x)^(3/2)/sqrt(a+b*x)
+--R
+--R
+--R 3 2 +-------+
+--R (d x + c x )\|d x + c
+--R (1) -----------------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1000
+r0:=1/64*(b*c-a*d)^2*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(5/2))+_
+ 1/96*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(b^3*d^2)-1/24*(3*b*c+7*a*d)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(b^2*d^2)+1/4*x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b*d)+_
+ 1/64*(b*c-a*d)*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^4*d^2)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 180a b c d + 54a b c d + 12a b c d + 9b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (- 56a b d + 72b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2 2 2
+--R (70a b d - 92a b c d + 6b c d)x - 105a d + 145a b c d - 15a b c d
+--R +
+--R 3 3
+--R - 9b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 2 +-+ +-+
+--R 192b d \|b \|d
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 1000
+--a0:=integrate(t0,x)
+--E 673
+
+--S 674 of 1000
+--m0:=a0-r0
+--E 674
+
+--S 675 of 1000
+--d0:=D(m0,x)
+--E 675
+
+)clear all
+
+--S 676 of 1000
+t0:=x*(c+d*x)^(3/2)/sqrt(a+b*x)
+--R
+--R
+--R 2 +-------+
+--R (d x + c x)\|d x + c
+--R (1) ----------------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1000
+r0:=-1/8*(b*c-a*d)^2*(b*c+5*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(7/2)*d^(3/2))-1/12*(b*c+5*a*d)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(b^2*d)+1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(b*d)-_
+ 1/8*(b*c-a*d)*(b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 15a d + 27a b c d - 9a b c d - 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R (8b d x + (- 10a b d + 14b c d)x + 15a d - 22a b c d + 3b c )\|b
+--R *
+--R +-+ +-------+ +-------+
+--R \|d \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24b d\|b \|d
+--R Type: Expression(Integer)
+--E 677
+
+--S 678 of 1000
+--a0:=integrate(t0,x)
+--E 678
+
+--S 679 of 1000
+--m0:=a0-r0
+--E 679
+
+--S 680 of 1000
+--d0:=D(m0,x)
+--E 680
+
+)clear all
+
+--S 681 of 1000
+t0:=(c+d*x)^(3/2)/sqrt(a+b*x)
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 681
+
+--S 682 of 1000
+r0:=3/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(5/2)*sqrt(d))+1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/b+3/4*(b*c-a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/b^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d - 6a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (2b d x - 3a d + 5b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4b \|b \|d
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1000
+--a0:=integrate(t0,x)
+--E 683
+
+--S 684 of 1000
+--m0:=a0-r0
+--E 684
+
+--S 685 of 1000
+--d0:=D(m0,x)
+--E 685
+
+)clear all
+
+--S 686 of 1000
+t0:=(c+d*x)^(3/2)/(x*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R +-------+
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1000
+r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(a)+_
+ (3*b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(d)/b^(3/2)+d*sqrt(a+b*x)*sqrt(c+d*x)/b
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ \|d \|b x + a
+--R (- a d + 3b c)\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ \|c \|b x + a +-+ +-+ +-------+ +-------+
+--R - 2b c\|b \|c atanh(--------------) + d\|a \|b \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|a \|d x + c
+--R /
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 688
+
+--S 689 of 1000
+--m0:=a0-r0
+--E 689
+
+--S 690 of 1000
+--d0:=D(m0,x)
+--E 690
+
+)clear all
+
+--S 691 of 1000
+t0:=(c+d*x)^(3/2)/(x^2*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R 2 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1000
+r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(b)+_
+ (b*c-3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(c)/a^(3/2)-(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x)+d*sqrt(a+b*x)*_
+ sqrt(c+d*x)/a
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ \|d \|b x + a
+--R 2a d x\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ \|c \|b x + a
+--R (- 3a d + b c)x\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R - c\|a \|b \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R a x\|a \|b
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 693
+
+--S 694 of 1000
+--m0:=a0-r0
+--E 694
+
+--S 695 of 1000
+--d0:=D(m0,x)
+--E 695
+
+)clear all
+
+--S 696 of 1000
+t0:=(c+d*x)^(3/2)/(x^3*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R 3 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1000
+r0:=-3/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(5/2)*sqrt(c))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^2)+_
+ 3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 3a d + 6a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R ((- 5a d + 3b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4a x \|a \|c
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1000
+--a0:=integrate(t0,x)
+--E 698
+
+--S 699 of 1000
+--m0:=a0-r0
+--E 699
+
+--S 700 of 1000
+--d0:=D(m0,x)
+--E 700
+
+)clear all
+
+--S 701 of 1000
+t0:=(c+d*x)^(3/2)/(x^4*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R 4 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1000
+r0:=1/8*(b*c-a*d)^2*(5*b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(7/2)*c^(3/2))-1/3*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (a*x^3)+1/12*(5*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^2)-_
+ 1/24*(15*b^2*c/a-22*b*d+3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (3a d + 9a b c d - 27a b c d + 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2
+--R ((- 3a d + 22a b c d - 15b c )x + (- 14a c d + 10a b c )x - 8a c )
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 1000
+--a0:=integrate(t0,x)
+--E 703
+
+--S 704 of 1000
+--m0:=a0-r0
+--E 704
+
+--S 705 of 1000
+--d0:=D(m0,x)
+--E 705
+
+)clear all
+
+--S 706 of 1000
+t0:=(c+d*x)^(3/2)/(x^5*sqrt(a+b*x))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R 5 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1000
+r0:=-1/64*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(5/2))-_
+ 1/4*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^4)+1/24*(7*b*c-3*a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^3)-1/96*(35*b^2*c/a-46*b*d+_
+ 3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^2)+1/192*(105*b^3*c^3-_
+ 145*a*b^2*c^2*d+15*a^2*b*c*d^2+9*a^3*d^3)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^4*c^2*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 9a d - 12a b c d - 54a b c d + 180a b c d - 105b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (9a d + 15a b c d - 145a b c d + 105b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3 3 3
+--R (- 6a c d + 92a b c d - 70a b c )x + (- 72a c d + 56a b c )x - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 4 2 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1000
+--a0:=integrate(t0,x)
+--E 708
+
+--S 709 of 1000
+--m0:=a0-r0
+--E 709
+
+--S 710 of 1000
+--d0:=D(m0,x)
+--E 710
+
+)clear all
+
+--S 711 of 1000
+t0:=x^2*(c+d*x)^(5/2)/sqrt(a+b*x)
+--R
+--R
+--R 2 4 3 2 2 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ---------------------------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1000
+r0:=1/128*(b*c-a*d)^3*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(5/2))+_
+ 1/192*(b*c-a*d)*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(b^4*d^2)+1/240*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*_
+ (c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*d^2)-3/40*(b*c+3*a*d)*_
+ (c+d*x)^(7/2)*sqrt(a+b*x)/(b^2*d^2)+1/5*x*(c+d*x)^(7/2)*_
+ sqrt(a+b*x)/(b*d)+1/128*(b*c-a*d)^2*(3*b^2*c^2+14*a*b*c*d+_
+ 63*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^2)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 945a d + 2625a b c d - 2250a b c d + 450a b c d + 75a b c d
+--R +
+--R 5 5
+--R 45b c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 4 4 3 4 4 3 3
+--R 384b d x + (- 432a b d + 1008b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 2
+--R (504a b d - 1184a b c d + 744b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4 4
+--R (- 630a b d + 1498a b c d - 962a b c d + 30b c d)x + 945a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 2310a b c d + 1564a b c d - 90a b c d - 45b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 5 2 +-+ +-+
+--R 1920b d \|b \|d
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1000
+--a0:=integrate(t0,x)
+--E 713
+
+--S 714 of 1000
+--m0:=a0-r0
+--E 714
+
+--S 715 of 1000
+--d0:=D(m0,x)
+--E 715
+
+)clear all
+
+--S 716 of 1000
+t0:=x*(c+d*x)^(5/2)/sqrt(a+b*x)
+--R
+--R
+--R 2 3 2 2 +-------+
+--R (d x + 2c d x + c x)\|d x + c
+--R (1) --------------------------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1000
+r0:=-5/64*(b*c-a*d)^3*(b*c+7*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(9/2)*d^(3/2))-5/96*(b*c-a*d)*(b*c+7*a*d)*_
+ (c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*d)-1/24*(b*c+7*a*d)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(b^2*d)+1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/(b*d)-_
+ 5/64*(b*c-a*d)^2*(b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 300a b c d + 270a b c d - 60a b c d - 15b c )
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 3 3 2 3 3 2 2
+--R 48b d x + (- 56a b d + 136b c d )x
+--R +
+--R 2 3 2 2 3 2 3 3 2 2
+--R (70a b d - 172a b c d + 118b c d)x - 105a d + 265a b c d
+--R +
+--R 2 2 3 3
+--R - 191a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 +-+ +-+
+--R 192b d\|b \|d
+--R Type: Expression(Integer)
+--E 717
+
+--S 718 of 1000
+--a0:=integrate(t0,x)
+--E 718
+
+--S 719 of 1000
+--m0:=a0-r0
+--E 719
+
+--S 720 of 1000
+--d0:=D(m0,x)
+--E 720
+
+)clear all
+
+--S 721 of 1000
+t0:=(c+d*x)^(5/2)/sqrt(a+b*x)
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R +-------+
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1000
+r0:=5/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(7/2)*sqrt(d))+5/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b^2+_
+ 1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/b+5/8*(b*c-a*d)^2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/b^3
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R (8b d x + (- 10a b d + 26b c d)x + 15a d - 40a b c d + 33b c )\|b
+--R *
+--R +-+ +-------+ +-------+
+--R \|d \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24b \|b \|d
+--R Type: Expression(Integer)
+--E 722
+
+-- (1 . failed) cannot be coerced to mode (SparseUnivariatePolynomial (Integer))
+--S 723 of 1000
+--a0:=integrate(t0,x)
+--E 723
+
+--S 724 of 1000
+--m0:=a0-r0
+--E 724
+
+--S 725 of 1000
+--d0:=D(m0,x)
+--E 725
+
+)clear all
+
+--S 726 of 1000
+t0:=(c+d*x)^(5/2)/(x*sqrt(a+b*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R +-------+
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1000
+r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(a)+_
+ 1/4*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(5/2)+_
+ 1/2*d*(c+d*x)^(3/2)*sqrt(a+b*x)/b+1/4*d*(7*b*c-3*a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/b^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-+ \|d \|b x + a
+--R (3a d - 10a b c d + 15b c )\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|c \|b x + a
+--R - 8b c \|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+ +-------+
+--R (2b d x - 3a d + 9b c d)\|a \|b \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4b \|a \|b
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1000 (non-algebraic residues)
+-- a0:=integrate(t0,x)
+--E 728
+
+--S 729 of 1000
+--m0:=a0-r0
+--E 729
+
+--S 730 of 1000
+--d0:=D(m0,x)
+--E 730
+
+)clear all
+
+--S 731 of 1000
+t0:=(c+d*x)^(5/2)/(x^2*sqrt(a+b*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 2 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1000
+r0:=c^(3/2)*(b*c-5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ a^(3/2)+d^(3/2)*(5*b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/b^(3/2)+d*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ a-(c+d*x)^(5/2)*sqrt(a+b*x)/(a*x)+d*(b*c+a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a*b)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|d \|b x + a
+--R (- a d + 5a b c d)x\|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ \|c \|b x + a
+--R (- 5a b c d + b c )x\|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+ +-------+
+--R (a d x - b c )\|a \|b \|b x + a \|d x + c
+--R /
+--R +-+ +-+
+--R a b x\|a \|b
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 733
+
+--S 734 of 1000
+--m0:=a0-r0
+--E 734
+
+--S 735 of 1000
+--d0:=D(m0,x)
+--E 735
+
+)clear all
+
+--S 736 of 1000
+t0:=(c+d*x)^(5/2)/(x^3*sqrt(a+b*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 3 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1000
+r0:=2*d^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(b)-_
+ 1/4*(3*b^2*c^2-10*a*b*c*d+15*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(5/2)+1/4*_
+ (3*b*c-5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*x)-1/2*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(a*x^2)-1/4*d*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/a^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 +-+ +-+ \|d \|b x + a
+--R 8a d x \|a \|d atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a
+--R (- 15a d + 10a b c d - 3b c )x \|b \|c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+ +-------+
+--R ((- 9a c d + 3b c )x - 2a c )\|a \|b \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4a x \|a \|b
+--R Type: Expression(Integer)
+--E 737
+
+--S 738 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 738
+
+--S 739 of 1000
+--m0:=a0-r0
+--E 739
+
+--S 740 of 1000
+--d0:=D(m0,x)
+--E 740
+
+)clear all
+
+--S 741 of 1000
+t0:=(c+d*x)^(5/2)/(x^4*sqrt(a+b*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 4 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 741
+
+--S 742 of 1000
+r0:=5/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(7/2)*sqrt(c))+5/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (a^2*x^2)-1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*x^3)-5/8*(b*c-a*d)^2*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^3*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2
+--R ((- 33a d + 40a b c d - 15b c )x + (- 26a c d + 10a b c )x - 8a c )
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 24a x \|a \|c
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1000
+--a0:=integrate(t0,x)
+--E 743
+
+--S 744 of 1000
+--m0:=a0-r0
+--E 744
+
+--S 745 of 1000
+--d0:=D(m0,x)
+--E 745
+
+)clear all
+
+--S 746 of 1000
+t0:=(c+d*x)^(5/2)/(x^5*sqrt(a+b*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 5 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1000
+r0:=-5/64*(b*c-a*d)^3*(7*b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(9/2)*c^(3/2))+1/24*(7*b*c-5*a*d)*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/(a^2*x^3)-1/4*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*x^4)-_
+ 1/96*(35*b^2*c^2-58*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_
+ (a^3*x^2)+1/192*(105*b^3*c^3-265*a*b^2*c^2*d+191*a^2*b*c*d^2-_
+ 15*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c*x)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d + 60a b c d - 270a b c d + 300a b c d - 105b c )x
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 15a d + 191a b c d - 265a b c d + 105b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 118a c d + 172a b c d - 70a b c )x + (- 136a c d + 56a b c )x
+--R +
+--R 3 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 4 4 +-+ +-+
+--R 192a c x \|a \|c
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1000
+--a0:=integrate(t0,x)
+--E 748
+
+--S 749 of 1000
+--m0:=a0-r0
+--E 749
+
+--S 750 of 1000
+--d0:=D(m0,x)
+--E 750
+
+)clear all
+
+--S 751 of 1000
+t0:=(c+d*x)^(5/2)/(x^6*sqrt(a+b*x))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 6 +-------+
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1000
+r0:=1/128*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*c^(5/2))+_
+ 1/40*(9*b*c-5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*x^4)-_
+ 1/5*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*x^5)-1/240*(63*b^2*c^2-_
+ 94*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*x^3)+_
+ 1/960*(315*b^3*c^3-749*a*b^2*c^2*d+481*a^2*b*c*d^2-_
+ 15*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c*x^2)-_
+ 1/1920*(945*b^4*c^4-2310*a*b^3*c^3*d+1564*a^2*b^2*c^2*d^2-_
+ 90*a^3*b*c*d^3-45*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^5*c^2*x)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 45a d - 75a b c d - 450a b c d + 2250a b c d - 2625a b c d
+--R +
+--R 5 5
+--R 945b c
+--R *
+--R +-+ +-------+
+--R 5 \|c \|b x + a
+--R x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (45a d + 90a b c d - 1564a b c d + 2310a b c d - 945b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 3
+--R (- 30a c d + 962a b c d - 1498a b c d + 630a b c )x
+--R +
+--R 4 2 2 3 3 2 2 4 2
+--R (- 744a c d + 1184a b c d - 504a b c )x
+--R +
+--R 4 3 3 4 4 4
+--R (- 1008a c d + 432a b c )x - 384a c
+--R *
+--R +-+ +-+ +-------+ +-------+
+--R \|a \|c \|b x + a \|d x + c
+--R /
+--R 5 2 5 +-+ +-+
+--R 1920a c x \|a \|c
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1000
+--a0:=integrate(t0,x)
+--E 753
+
+--S 754 of 1000
+--m0:=a0-r0
+--E 754
+
+--S 755 of 1000
+--d0:=D(m0,x)
+--E 755
+
+)clear all
+
+--S 756 of 1000
+t0:=x^3/(sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 756
+
+--S 757 of 1000
+r0:=1/8*(b*c+a*d)*(12*a*b*c*d-5*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-1/24*(16*a*b*c*d-_
+ 15*(b*c+a*d)^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3)-5/12*(b*c+a*d)*_
+ x*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2)+1/3*x^2*sqrt(a+b*x)*sqrt(c+d*x)/(b*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 15a d - 9a b c d - 9a b c d - 15b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R (8b d x + (- 10a b d - 10b c d)x + 15a d + 14a b c d + 15b c )\|b
+--R *
+--R +-+ +-------+ +-------+
+--R \|d \|b x + a \|d x + c
+--R /
+--R 3 3 +-+ +-+
+--R 24b d \|b \|d
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1000
+--a0:=integrate(t0,x)
+--E 758
+
+--S 759 of 1000
+--m0:=a0-r0
+--E 759
+
+--S 760 of 1000
+--d0:=D(m0,x)
+--E 760
+
+)clear all
+
+--S 761 of 1000
+t0:=x^2/(sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 761
+
+--S 762 of 1000
+r0:=-1/4*(4*a*b*c*d-3*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-3/4*(b*c+a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2)+1/2*x*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b*d)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d + 2a b c d + 3b c )atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R (2b d x - 3a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4b d \|b \|d
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1000
+--a0:=integrate(t0,x)
+--E 763
+
+--S 764 of 1000
+--m0:=a0-r0
+--E 764
+
+--S 765 of 1000
+--d0:=D(m0,x)
+--E 765
+
+)clear all
+
+--S 766 of 1000
+t0:=x/(sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R x
+--R (1) --------------------
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1000
+r0:=-(b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*_
+ d^(3/2))+sqrt(a+b*x)*sqrt(c+d*x)/(b*d)
+--R
+--R
+--R +-+ +-------+
+--R \|d \|b x + a +-+ +-+ +-------+ +-------+
+--R (- a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|b \|d x + c
+--R (2) -----------------------------------------------------------------
+--R +-+ +-+
+--R b d\|b \|d
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1000
+--a0:=integrate(t0,x)
+--E 768
+
+--S 769 of 1000
+--m0:=a0-r0
+--E 769
+
+--S 770 of 1000
+--d0:=D(m0,x)
+--E 770
+
+)clear all
+
+--S 771 of 1000
+t0:=1/(sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 1
+--R (1) --------------------
+--R +-------+ +-------+
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1000
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))
+--R
+--R
+--R +-+ +-------+
+--R \|d \|b x + a
+--R 2atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R (2) ----------------------
+--R +-+ +-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1000
+--a0:=integrate(t0,x)
+--E 773
+
+--S 774 of 1000
+--m0:=a0-r0
+--E 774
+
+--S 775 of 1000
+--d0:=D(m0,x)
+--E 775
+
+)clear all
+
+--S 776 of 1000
+t0:=1/(x*sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +-------+ +-------+
+--R x\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(sqrt(a)*sqrt(c))
+--R
+--R
+--R +-+ +-------+
+--R \|c \|b x + a
+--R 2atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R (2) - ----------------------
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1000
+--a0:=integrate(t0,x)
+--E 778
+
+--S 779 of 1000
+--m0:=a0-r0
+--E 779
+
+--S 780 of 1000
+--d0:=D(m0,x)
+--E 780
+
+)clear all
+
+--S 781 of 1000
+t0:=1/(x^2*sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 +-------+ +-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1000
+r0:=(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(3/2)*c^(3/2))-sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x)
+--R
+--R
+--R +-+ +-------+
+--R \|c \|b x + a +-+ +-+ +-------+ +-------+
+--R (a d + b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c
+--R +-+ +-------+
+--R \|a \|d x + c
+--R (2) -----------------------------------------------------------------
+--R +-+ +-+
+--R a c x\|a \|c
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1000
+--a0:=integrate(t0,x)
+--E 783
+
+--S 784 of 1000
+--m0:=a0-r0
+--E 784
+
+--S 785 of 1000
+--d0:=D(m0,x)
+--E 785
+
+)clear all
+
+--S 786 of 1000
+t0:=1/(x^3*sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 3 +-------+ +-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1000
+r0:=-1/4*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/2*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a*c*x^2)+3/4*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 \|c \|b x + a
+--R (- 3a d - 2a b c d - 3b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+ +-------+
+--R ((3a d + 3b c)x - 2a c)\|a \|c \|b x + a \|d x + c
+--R /
+--R 2 2 2 +-+ +-+
+--R 4a c x \|a \|c
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1000
+--a0:=integrate(t0,x)
+--E 788
+
+--S 789 of 1000
+--m0:=a0-r0
+--E 789
+
+--S 790 of 1000
+--d0:=D(m0,x)
+--E 790
+
+)clear all
+
+--S 791 of 1000
+t0:=1/(x^4*sqrt(a+b*x)*sqrt(c+d*x))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 4 +-------+ +-------+
+--R x \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1000
+r0:=1/8*(b*c+a*d)*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_
+ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_
+ 1/3*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^3)+5/12*(b*c+a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(a^2*c^2*x^2)-1/24*(15*b^2*c^2+14*a*b*c*d+15*a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a
+--R (15a d + 9a b c d + 9a b c d + 15b c )x atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((- 15a d - 14a b c d - 15b c )x + (10a c d + 10a b c )x - 8a c )\|a
+--R *
+--R +-+ +-------+ +-------+
+--R \|c \|b x + a \|d x + c
+--R /
+--R 3 3 3 +-+ +-+
+--R 24a c x \|a \|c
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1000
+--a0:=integrate(t0,x)
+--E 793
+
+--S 794 of 1000
+--m0:=a0-r0
+--E 794
+
+--S 795 of 1000
+--d0:=D(m0,x)
+--E 795
+
+)clear all
+
+--S 796 of 1000
+t0:=x^3/((c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------------------
+--R +-------+ +-------+
+--R (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1000
+r0:=3/4*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))+1/2*x^2*sqrt(a+b*x)/_
+ (b*d*sqrt(c+d*x))+1/2*c*(4*a*c+(5*b*c+3*a*d)*x)*sqrt(a+b*x)/_
+ (b*d^2*(b*c-a*d)*sqrt(c+d*x))-1/4*(3*b*c-a*d)*(5*b*c+3*a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 3 2 2 2 2 3 3 +-------+ \|d \|b x + a
+--R (3a d + 3a b c d + 9a b c d - 15b c )\|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 2 2 2 2 3 2 2 2 2 2
+--R (2a b d - 2b c d )x + (- 3a d - 2a b c d + 5b c d)x - 3a c d
+--R +
+--R 2 2 3
+--R - 4a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 2 4 3 3 +-+ +-+ +-------+
+--R (4a b d - 4b c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 797
+
+--S 798 of 1000
+--a0:=integrate(t0,x)
+--E 798
+
+--S 799 of 1000
+--m0:=a0-r0
+--E 799
+
+--S 800 of 1000
+--d0:=D(m0,x)
+--E 800
+
+)clear all
+
+--S 801 of 1000
+t0:=x^2/((c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------------
+--R +-------+ +-------+
+--R (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1000
+r0:=-(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(3/2)*d^(5/2))+2*c^2*sqrt(a+b*x)/(d^2*(b*c-a*d)*sqrt(c+d*x))+_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ \|d \|b x + a
+--R (- a d - 2a b c d + 3b c )\|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+
+--R ((a d - b c d)x + a c d - 3b c )\|b \|d \|b x + a
+--R /
+--R 3 2 2 +-+ +-+ +-------+
+--R (a b d - b c d )\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1000
+--a0:=integrate(t0,x)
+--E 803
+
+--S 804 of 1000
+--m0:=a0-r0
+--E 804
+
+--S 805 of 1000
+--d0:=D(m0,x)
+--E 805
+
+)clear all
+
+--S 806 of 1000
+t0:=x/((c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R x
+--R (1) -----------------------------
+--R +-------+ +-------+
+--R (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1000
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(3/2)*sqrt(b))-_
+ 2*c*sqrt(a+b*x)/(d*(b*c-a*d)*sqrt(c+d*x))
+--R
+--R
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a +-+ +-+ +-------+
+--R (2a d - 2b c)\|d x + c atanh(--------------) + 2c\|b \|d \|b x + a
+--R +-+ +-------+
+--R \|b \|d x + c
+--R (2) -------------------------------------------------------------------
+--R 2 +-+ +-+ +-------+
+--R (a d - b c d)\|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1000
+--a0:=integrate(t0,x)
+--E 808
+
+--S 809 of 1000
+--m0:=a0-r0
+--E 809
+
+--S 810 of 1000
+--d0:=D(m0,x)
+--E 810
+
+)clear all
+
+--S 811 of 1000
+t0:=1/((c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------
+--R +-------+ +-------+
+--R (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1000
+r0:=2*sqrt(a+b*x)/((b*c-a*d)*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R 2\|b x + a
+--R (2) - ---------------------
+--R +-------+
+--R (a d - b c)\|d x + c
+--R Type: Expression(Integer)
+--E 812
+
+--S 813 of 1000 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-------+ 2
+--R - 4c\|b x + a \|d x + c + (- c - 4a)d x - c - 4a c
+--R (3) ----------------------------------------------------
+--R 2 2 2 3
+--R (2a c d - 2b c d)x + 2a c d - 2b c
+--R Type: Union(Expression(Integer),...)
+--E 813
+
+--S 814 of 1000 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R - c - 4a
+--R (4) --------------
+--R 2
+--R 2a c d - 2b c
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1000
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 815
+
+)clear all
+
+--S 816 of 1000
+t0:=1/(x*(c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 2 +-------+ +-------+
+--R (d x + c x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*sqrt(a))-_
+ 2*d*sqrt(a+b*x)/(c*(b*c-a*d)*sqrt(c+d*x))
+--R
+--R
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a +-+ +-+ +-------+
+--R (- 2a d + 2b c)\|d x + c atanh(--------------) + 2d\|a \|c \|b x + a
+--R +-+ +-------+
+--R \|a \|d x + c
+--R (2) ---------------------------------------------------------------------
+--R 2 +-+ +-+ +-------+
+--R (a c d - b c )\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1000
+--a0:=integrate(t0,x)
+--E 818
+
+--S 819 of 1000
+--m0:=a0-r0
+--E 819
+
+--S 820 of 1000
+--d0:=D(m0,x)
+--E 820
+
+)clear all
+
+--S 821 of 1000
+t0:=1/(x^2*(c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 3 2 +-------+ +-------+
+--R (d x + c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1000
+r0:=(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(3/2)*c^(5/2))-d*(b*c-3*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)*_
+ sqrt(c+d*x))-sqrt(a+b*x)/(a*c*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ \|c \|b x + a
+--R (3a d - 2a b c d - b c )x\|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 +-+ +-+ +-------+
+--R ((- 3a d + b c d)x - a c d + b c )\|a \|c \|b x + a
+--R /
+--R 2 2 3 +-+ +-+ +-------+
+--R (a c d - a b c )x\|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1000
+--a0:=integrate(t0,x)
+--E 823
+
+--S 824 of 1000
+--m0:=a0-r0
+--E 824
+
+--S 825 of 1000
+--d0:=D(m0,x)
+--E 825
+
+)clear all
+
+--S 826 of 1000
+t0:=1/(x^3*(c+d*x)^(3/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 4 3 +-------+ +-------+
+--R (d x + c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 826
+
+--S 827 of 1000
+r0:=-3/4*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))+1/4*d*(3*b*c-5*a*d)*_
+ (b*c+3*a*d)*sqrt(a+b*x)/(a^2*c^3*(b*c-a*d)*sqrt(c+d*x))-_
+ 1/2*sqrt(a+b*x)/(a*c*x^2*sqrt(c+d*x))+1/4*(3*b*c+5*a*d)*_
+ sqrt(a+b*x)/(a^2*c^2*x*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 2 +-------+
+--R (- 15a d + 9a b c d + 3a b c d + 3b c )x \|d x + c
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R (15a d - 4a b c d - 3b c d)x + (5a c d - 2a b c d - 3b c )x
+--R +
+--R 2 2 3
+--R - 2a c d + 2a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 3 3 2 4 2 +-+ +-+ +-------+
+--R (4a c d - 4a b c )x \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1000
+--a0:=integrate(t0,x)
+--E 828
+
+--S 829 of 1000
+--m0:=a0-r0
+--E 829
+
+--S 830 of 1000
+--d0:=D(m0,x)
+--E 830
+
+)clear all
+
+--S 831 of 1000
+t0:=x^4/((c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 4
+--R x
+--R (1) ----------------------------------------
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1000
+r0:=1/4*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(9/2))+1/6*c*(7*b*c-3*a*d)*x^2*_
+ sqrt(a+b*x)/(b*d^2*(b*c-a*d)*(c+d*x)^(3/2))+1/2*x^3*sqrt(a+b*x)/_
+ (b*d*(c+d*x)^(3/2))+1/6*c*(4*a*c*(7*b*c-3*a*d)+(35*b^2*c^2-_
+ 18*a*b*c*d-9*a^2*d^2)*x)*sqrt(a+b*x)/(b*d^3*(b*c-a*d)^2*sqrt(c+d*x))-_
+ 1/12*(3*b*c-a*d)*(35*b^2*c^2-18*a*b*c*d-9*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^2*d^4*(b*c-a*d)^2)
+--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 + 54a b c d - 180a b c d + 105b c d)x + 9a c d
+--R +
+--R 3 2 3 2 2 3 2 3 4 4 5
+--R 12a b c d + 54a b c d - 180a b c d + 105b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 3
+--R (6a b d - 12a b c d + 6b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 2
+--R (- 9a d - 3a b c d + 33a b c d - 21b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 3 2 3
+--R (- 18a c d - 24a b c d + 198a b c d - 140b c d)x - 9a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 15a b c d + 145a b c d - 105b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 2 2 7 3 6 4 2 5 2 2 6 3 2 5
+--R (12a b d - 24a b c d + 12b c d )x + 12a b c d - 24a b c d
+--R +
+--R 4 3 4
+--R 12b c d
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1000
+--a0:=integrate(t0,x)
+--E 833
+
+--S 834 of 1000
+--m0:=a0-r0
+--E 834
+
+--S 835 of 1000
+--d0:=D(m0,x)
+--E 835
+
+)clear all
+
+--S 836 of 1000
+t0:=x^3/((c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------------------
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1000
+r0:=-(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(3/2)*d^(7/2))+x^2*sqrt(a+b*x)/(b*d*(c+d*x)^(3/2))+_
+ 1/3*c*(4*a*c+(5*b*c+a*d)*x)*sqrt(a+b*x)/(b*d^2*(b*c-a*d)*_
+ (c+d*x)^(3/2))+1/3*c*(5*b*c-7*a*d)*(3*b*c-a*d)*sqrt(a+b*x)/_
+ (b*d^3*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2
+--R (- 3a d - 9a b c d + 27a b c d - 15b c d)x - 3a c d - 9a b c d
+--R +
+--R 2 3 3 4
+--R 27a b c d - 15b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (3a d - 6a b c d + 3b c d )x + (6a c d - 30a b c d + 20b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d - 22a b c d + 15b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|b x + a
+--R /
+--R 2 6 2 5 3 2 4 2 5 2 2 4 3 3 3 +-+
+--R ((3a b d - 6a b c d + 3b c d )x + 3a b c d - 6a b c d + 3b c d )\|b
+--R *
+--R +-+ +-------+
+--R \|d \|d x + c
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1000
+--a0:=integrate(t0,x)
+--E 838
+
+--S 839 of 1000
+--m0:=a0-r0
+--E 839
+
+--S 840 of 1000
+--d0:=D(m0,x)
+--E 840
+
+)clear all
+
+--S 841 of 1000
+t0:=x^2/((c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------------------
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1000
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(5/2)*sqrt(b))+_
+ 2/3*c^2*sqrt(a+b*x)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))-_
+ 4/3*c*(2*b*c-3*a*d)*sqrt(a+b*x)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 3
+--R ((6a d - 12a b c d + 6b c d)x + 6a c d - 12a b c d + 6b c )
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 3 +-+ +-+ +-------+
+--R ((12a c d - 8b c d)x + 10a c d - 6b c )\|b \|d \|b x + a
+--R /
+--R 2 5 4 2 2 3 2 4 2 3 2 3 2 +-+ +-+
+--R ((3a d - 6a b c d + 3b c d )x + 3a c d - 6a b c d + 3b c d )\|b \|d
+--R *
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 842
+
+--S 843 of 1000
+--a0:=integrate(t0,x)
+--E 843
+
+--S 844 of 1000
+--m0:=a0-r0
+--E 844
+
+--S 845 of 1000
+--d0:=D(m0,x)
+--E 845
+
+)clear all
+
+--S 846 of 1000
+t0:=x/((c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R x
+--R (1) ----------------------------------------
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1000
+r0:=-2/3*c*sqrt(a+b*x)/(d*(b*c-a*d)*(c+d*x)^(3/2))+2/3*(b*c-3*a*d)*_
+ sqrt(a+b*x)/(d*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R ((- 6a d + 2b c)x - 4a c)\|b x + a
+--R (2) ----------------------------------------------------------------------
+--R 2 3 2 2 2 2 2 2 2 3 +-------+
+--R ((3a d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )\|d x + c
+--R Type: Expression(Integer)
+--E 847
+
+--S 848 of 1000 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 +-------+ +-------+ 2 2 2
+--R ((- 6a c d + 2b c )x - 4a c )\|b x + a \|d x + c + (- a c - 4a )d x
+--R +
+--R 2 2 3 2 2
+--R (- 2a c - 8a c)d x - a c - 4a c
+--R /
+--R 2 4 2 3 2 3 2 2 2 2 3 3 2 2 4
+--R (3a c d - 6a b c d + 3b c d )x + (6a c d - 12a b c d + 6b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R 3a c d - 6a b c d + 3b c
+--R Type: Union(Expression(Integer),...)
+--E 848
+
+--S 849 of 1000 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2
+--R - a c - 4a
+--R (4) --------------------------
+--R 2 2 2 2 3
+--R 3a c d - 6a b c d + 3b c
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1000
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 850
+
+)clear all
+
+--S 851 of 1000
+t0:=1/((c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------
+--R 2 2 2 +-------+ +-------+
+--R (d x + 2c d x + c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1000
+r0:=2/3*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(3/2))+4/3*b*sqrt(a+b*x)/_
+ ((b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R +-------+
+--R (4b d x - 2a d + 6b c)\|b x + a
+--R (2) ----------------------------------------------------------------------
+--R 2 3 2 2 2 2 2 2 2 3 +-------+
+--R ((3a d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )\|d x + c
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1000 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 +-------+ +-------+
+--R (20b c d x - 10a c d + 30b c )\|b x + a \|d x + c
+--R +
+--R 2 3 2 2 2
+--R ((- a c - 25a )d + (3b c + 75a b c)d )x
+--R +
+--R 2 2 2 3 2 3 2 2
+--R ((- 2a c - 50a c)d + (6b c + 150a b c )d)x + (- a c - 25a c )d
+--R +
+--R 4 3
+--R 3b c + 75a b c
+--R /
+--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5
+--R (15a c d - 30a b c d + 15b c d )x + (30a c d - 60a b c d + 30b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R 15a c d - 30a b c d + 15b c
+--R Type: Union(Expression(Integer),...)
+--E 853
+
+--S 854 of 1000 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R (- a c - 25a )d + 3b c + 75a b c
+--R (4) ---------------------------------
+--R 2 2 2 3 2 4
+--R 15a c d - 30a b c d + 15b c
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1000
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 855
+
+)clear all
+
+--S 856 of 1000
+t0:=1/(x*(c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------
+--R 2 3 2 2 +-------+ +-------+
+--R (d x + 2c d x + c x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*sqrt(a))-_
+ 2/3*d*sqrt(a+b*x)/(c*(b*c-a*d)*(c+d*x)^(3/2))-_
+ 2/3*d*(5*b*c-3*a*d)*sqrt(a+b*x)/(c^2*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 3
+--R ((- 6a d + 12a b c d - 6b c d)x - 6a c d + 12a b c d - 6b c )
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 2 2 2 +-+ +-+ +-------+
+--R ((6a d - 10b c d )x + 8a c d - 12b c d)\|a \|c \|b x + a
+--R /
+--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +-+ +-+
+--R ((3a c d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )\|a \|c
+--R *
+--R +-------+
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 857
+
+--S 858 of 1000
+--a0:=integrate(t0,x)
+--E 858
+
+--S 859 of 1000
+--m0:=a0-r0
+--E 859
+
+--S 860 of 1000
+--d0:=D(m0,x)
+--E 860
+
+)clear all
+
+--S 861 of 1000
+t0:=1/(x^2*(c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R 2 4 3 2 2 +-------+ +-------+
+--R (d x + 2c d x + c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1000
+r0:=(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(3/2)*c^(7/2))-1/3*d*(3*b*c-5*a*d)*sqrt(a+b*x)/_
+ (a*c^2*(b*c-a*d)*(c+d*x)^(3/2))-sqrt(a+b*x)/(a*c*x*(c+d*x)^(3/2))-_
+ 1/3*d*(3*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)/_
+ (a*c^3*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 2
+--R (15a d - 27a b c d + 9a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (15a c d - 27a b c d + 9a b c d + 3b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 4 3 2 2 2 2
+--R (- 15a d + 22a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 3 2 4
+--R (- 20a c d + 30a b c d - 6b c d)x - 3a c d + 6a b c d - 3b c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 3 3 3 2 4 2 2 5 2 3 4 2 2 5 2 6
+--R ((3a c d - 6a b c d + 3a b c d)x + (3a c d - 6a b c d + 3a b c )x)
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1000
+--a0:=integrate(t0,x)
+--E 863
+
+--S 864 of 1000
+--m0:=a0-r0
+--E 864
+
+--S 865 of 1000
+--d0:=D(m0,x)
+--E 865
+
+)clear all
+
+--S 866 of 1000
+t0:=1/(x^3*(c+d*x)^(5/2)*sqrt(a+b*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R 2 5 4 2 3 +-------+ +-------+
+--R (d x + 2c d x + c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1000
+r0:=-1/4*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(9/2))+1/12*d*(9*b^2*c^2+_
+ 18*a*b*c*d-35*a^2*d^2)*sqrt(a+b*x)/(a^2*c^3*(b*c-a*d)*(c+d*x)^(3/2))-_
+ 1/2*sqrt(a+b*x)/(a*c*x^2*(c+d*x)^(3/2))+1/4*(3*b*c+7*a*d)*_
+ sqrt(a+b*x)/(a^2*c^2*x*(c+d*x)^(3/2))+1/12*d*(9*b^3*c^3+_
+ 15*a*b^2*c^2*d-145*a^2*b*c*d^2+105*a^3*d^3)*sqrt(a+b*x)/_
+ (a^2*c^4*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (- 105a d + 180a b c d - 54a 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 2
+--R (- 105a c d + 180a b c d - 54a b c d - 12a b c d - 9b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 3
+--R (105a d - 145a b c d + 15a b c d + 9b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (140a c d - 198a b c d + 24a b c d + 18b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 3 3 2 2 4
+--R (21a c d - 33a b c d + 3a b c d + 9b c )x - 6a c d + 12a b c d
+--R +
+--R 2 5
+--R - 6a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|b x + a
+--R /
+--R 4 4 3 3 5 2 2 2 6 3
+--R (12a c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 5 2 3 6 2 2 7 2
+--R (12a c d - 24a b c d + 12a b c )x
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1000
+--a0:=integrate(t0,x)
+--E 868
+
+--S 869 of 1000
+--m0:=a0-r0
+--E 869
+
+--S 870 of 1000
+--d0:=D(m0,x)
+--E 870
+
+)clear all
+
+--S 871 of 1000
+t0:=1/(x*sqrt(1-a-b*x)*sqrt(1+a+b*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R +-------------+ +-----------+
+--R x\|- b x - a + 1 \|b x + a + 1
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1000
+r0:=-2*atanh(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(1-a-b*x)))/sqrt(1-a^2)
+--R
+--R
+--R +-------+ +-----------+
+--R \|- a + 1 \|b x + a + 1
+--R 2atanh(------------------------)
+--R +-------------+ +-----+
+--R \|- b x - a + 1 \|a + 1
+--R (2) - --------------------------------
+--R +--------+
+--R | 2
+--R \|- a + 1
+--R Type: Expression(Integer)
+--E 872
+
+--S 873 of 1000
+--a0:=integrate(t0,x)
+--E 873
+
+--S 874 of 1000
+--m0:=a0-r0
+--E 874
+
+--S 875 of 1000
+--d0:=D(m0,x)
+--E 875
+
+)clear all
+
+--S 876 of 1000
+t0:=x^3*(c+d*x)^(3/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 4 3 +-------+
+--R (d x + c x )\|d x + c
+--R (1) -----------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1000
+r0:=3/64*(b*c-a*d)*(b^3*c^3+5*a*b^2*c^2*d+35*a^2*b*c*d^2-105*a^3*d^3)*_
+ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(5/2))-_
+ 2*x^3*(c+d*x)^(3/2)/(b*sqrt(a+b*x))-1/32*(3*b^2*c^2+14*a*b*c*d-_
+ 105*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^4*d^2)+1/8*(b*c-21*a*d)*_
+ x*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*d)+9/4*x^2*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/b^2+3/64*(b^3*c^3+5*a*b^2*c^2*d+35*a^2*b*c*d^2-_
+ 105*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^2)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-------+
+--R (315a d - 420a b c d + 90a b c d + 12a b c d + 3b c )\|b x + a
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 3 4 3 3 4 2 3
+--R 16b d x + (- 24a b d + 24b c d )x
+--R +
+--R 2 2 3 3 2 4 2 2
+--R (42a b d - 44a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 4 3
+--R (- 105a b d + 119a b c d - 11a b c d - 3b c )x - 315a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 315a b c d - 13a b c d - 3a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 5 2 +-+ +-+ +-------+
+--R 64b d \|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1000
+--a0:=integrate(t0,x)
+--E 878
+
+--S 879 of 1000
+--m0:=a0-r0
+--E 879
+
+--S 880 of 1000
+--d0:=D(m0,x)
+--E 880
+
+)clear all
+
+--S 881 of 1000
+t0:=x^2*(c+d*x)^(3/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 3 2 +-------+
+--R (d x + c x )\|d x + c
+--R (1) -----------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1000
+r0:=-1/8*(b*c-a*d)*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(3/2))-_
+ 2*a^2*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-_
+ 1/12*(10*a*c+b*c^2/d-35*a^2*d/b)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (b^2*(b*c-a*d))+1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*d)-_
+ 1/8*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-------+
+--R (- 105a d + 135a b c d - 27a b c d - 3b c )\|b x + a
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 2 3 2 2 3 2 2 2 2 3 2
+--R 8b d x + (- 14a b d + 14b c d)x + (35a b d - 38a b c d + 3b c )x
+--R +
+--R 3 2 2 2 2
+--R 105a d - 100a b c d + 3a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 4 +-+ +-+ +-------+
+--R 24b d\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1000
+--a0:=integrate(t0,x)
+--E 883
+
+--S 884 of 1000
+--m0:=a0-r0
+--E 884
+
+--S 885 of 1000
+--d0:=D(m0,x)
+--E 885
+
+)clear all
+
+--S 886 of 1000
+t0:=x*(c+d*x)^(3/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 2 +-------+
+--R (d x + c x)\|d x + c
+--R (1) ----------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1000
+r0:=3/4*(b*c-5*a*d)*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(7/2)*sqrt(d))+2*a*(c+d*x)^(5/2)/(b*(b*c-a*d)*_
+ sqrt(a+b*x))+1/2*(b*c-5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (b^2*(b*c-a*d))+3/4*(b*c-5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^3
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ \|d \|b x + a
+--R (15a d - 18a b c d + 3b c )\|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+
+--R (2b d x + (- 5a b d + 5b c)x - 15a d + 13a b c)\|b \|d \|d x + c
+--R /
+--R 3 +-+ +-+ +-------+
+--R 4b \|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1000
+--a0:=integrate(t0,x)
+--E 888
+
+--S 889 of 1000
+--m0:=a0-r0
+--E 889
+
+--S 890 of 1000
+--d0:=D(m0,x)
+--E 890
+
+)clear all
+
+--S 891 of 1000
+t0:=(c+d*x)^(3/2)/(a+b*x)^(3/2)
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1000
+r0:=3*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(d)/b^(5/2)-2*(c+d*x)^(3/2)/(b*sqrt(a+b*x))+3*d*_
+ sqrt(a+b*x)*sqrt(c+d*x)/b^2
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-------+ \|d \|b x + a
+--R (- 3a d + 3b c)\|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R (b d x + 3a d - 2b c)\|b \|d x + c
+--R /
+--R 2 +-+ +-------+
+--R b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1000
+--a0:=integrate(t0,x)
+--E 893
+
+--S 894 of 1000
+--m0:=a0-r0
+--E 894
+
+--S 895 of 1000
+--d0:=D(m0,x)
+--E 895
+
+)clear all
+
+--S 896 of 1000
+t0:=(c+d*x)^(3/2)/(x*(a+b*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) ----------------------
+--R 2 +-------+
+--R (b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 1000
+r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(3/2)+_
+ 2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(3/2)+_
+ 2*(c+d*x)^(3/2)/(a*sqrt(a+b*x))-2*d*sqrt(a+b*x)*sqrt(c+d*x)/(a*b)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ +-------+ \|d \|b x + a
+--R 2a d\|a \|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R +-+ +-+ +-------+ \|c \|b x + a
+--R - 2b c\|b \|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-+ +-------+
+--R (- 2a d + 2b c)\|a \|b \|d x + c
+--R /
+--R +-+ +-+ +-------+
+--R a b\|a \|b \|b x + a
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 898
+
+--S 899 of 1000
+--m0:=a0-r0
+--E 899
+
+--S 900 of 1000
+--d0:=D(m0,x)
+--E 900
+
+)clear all
+
+--S 901 of 1000
+t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -----------------------
+--R 3 2 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 1000
+r0:=3*(b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(c)/a^(5/2)-(c+d*x)^(3/2)/(a*x*sqrt(a+b*x))-3*(b*c-a*d)*_
+ sqrt(c+d*x)/(a^2*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-------+ \|c \|b x + a
+--R (- 3a d + 3b c)x\|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R +-+ +-------+
+--R ((2a d - 3b c)x - a c)\|a \|d x + c
+--R /
+--R 2 +-+ +-------+
+--R a x\|a \|b x + a
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1000
+--a0:=integrate(t0,x)
+--E 903
+
+--S 904 of 1000
+--m0:=a0-r0
+--E 904
+
+--S 905 of 1000
+--d0:=D(m0,x)
+--E 905
+
+)clear all
+
+--S 906 of 1000
+t0:=(c+d*x)^(3/2)/(x^3*(a+b*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -----------------------
+--R 4 3 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1000
+r0:=-3/4*(b*c-a*d)*(5*b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*sqrt(c))-1/2*(c+d*x)^(3/2)/_
+ (a*x^2*sqrt(a+b*x))+1/4*b*(15*b*c-13*a*d)*sqrt(c+d*x)/_
+ (a^3*sqrt(a+b*x))+1/4*(5*b*c-3*a*d)*sqrt(c+d*x)/(a^2*x*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-------+ \|c \|b x + a
+--R (- 3a d + 18a b c d - 15b c )x \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 +-+ +-+ +-------+
+--R ((- 13a b d + 15b c)x + (- 5a d + 5a b c)x - 2a c)\|a \|c \|d x + c
+--R /
+--R 3 2 +-+ +-+ +-------+
+--R 4a x \|a \|c \|b x + a
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1000
+--a0:=integrate(t0,x)
+--E 908
+
+--S 909 of 1000
+--m0:=a0-r0
+--E 909
+
+--S 910 of 1000
+--d0:=D(m0,x)
+--E 910
+
+)clear all
+
+--S 911 of 1000
+t0:=(c+d*x)^(3/2)/(x^4*(a+b*x)^(3/2))
+--R
+--R
+--R +-------+
+--R (d x + c)\|d x + c
+--R (1) -----------------------
+--R 5 4 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1000
+r0:=1/8*(b*c-a*d)*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(3/2))-1/3*(c+d*x)^(3/2)/_
+ (a*x^3*sqrt(a+b*x))-1/24*b*(105*b^2*c^2-100*a*b*c*d+3*a^2*d^2)*_
+ sqrt(c+d*x)/(a^4*c*sqrt(a+b*x))+1/12*(7*b*c-3*a*d)*sqrt(c+d*x)/_
+ (a^2*x^2*sqrt(a+b*x))-1/24*(35*b*c-3*a*d)*(b*c-a*d)*_
+ sqrt(c+d*x)/(a^3*c*x*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 3 +-------+
+--R (3a d + 27a b c d - 135a b c d + 105b c )x \|b x + a
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 3 2 3
+--R (- 3a b d + 100a b c d - 105b c )x
+--R +
+--R 3 2 2 2 2 2 3 2 2 3 2
+--R (- 3a d + 38a b c d - 35a b c )x + (- 14a c d + 14a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R /
+--R 4 3 +-+ +-+ +-------+
+--R 24a c x \|a \|c \|b x + a
+--R Type: Expression(Integer)
+--E 912
+
+--S 913 of 1000
+--a0:=integrate(t0,x)
+--E 913
+
+--S 914 of 1000
+--m0:=a0-r0
+--E 914
+
+--S 915 of 1000
+--d0:=D(m0,x)
+--E 915
+
+)clear all
+
+--S 916 of 1000
+t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 2 5 4 2 3 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ---------------------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1000
+r0:=3/128*(b*c-a*d)^2*(b^3*c^3+7*a*b^2*c^2*d+63*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^(5/2))-_
+ 2*x^3*(c+d*x)^(5/2)/(b*sqrt(a+b*x))+1/64*(b^3*c^3+7*a*b^2*c^2*d+_
+ 63*a^2*b*c*d^2-231*a^3*d^3)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^5*d^2)-_
+ 1/80*(5*b^2*c^2+30*a*b*c*d-231*a^2*d^2)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(b^4*d^2)+1/40*(5*b*c-99*a*d)*x*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(b^3*d)+11/5*x^2*(c+d*x)^(5/2)*sqrt(a+b*x)/b^2+_
+ 3/128*(b*c-a*d)*(b^3*c^3+7*a*b^2*c^2*d+63*a^2*b*c*d^2-231*_
+ a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^6*d^2)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 3465a d + 7875a b c d - 5250a b c d + 750a b c d + 75a b c d
+--R +
+--R 5 5
+--R 15b c
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 5 4 5 4 4 5 3 4
+--R 128b d x + (- 176a b d + 336b c d )x
+--R +
+--R 2 3 4 4 3 5 2 2 3
+--R (264a b d - 512a b c d + 248b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 2
+--R (- 462a b d + 918a b c d - 466a b c d + 10b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R (1155a b d - 2394a b c d + 1324a b c d - 70a b c d - 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3465a d - 6720a b c d + 3318a b c d - 80a b c d - 15a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 6 2 +-+ +-+ +-------+
+--R 640b d \|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 917
+
+--S 918 of 1000
+--a0:=integrate(t0,x)
+--E 918
+
+--S 919 of 1000
+--m0:=a0-r0
+--E 919
+
+--S 920 of 1000
+--d0:=D(m0,x)
+--E 920
+
+)clear all
+
+--S 921 of 1000
+t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 2 4 3 2 2 +-------+
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ---------------------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1000
+r0:=-5/64*(b*c-a*d)^2*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(3/2))-_
+ 2*a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-_
+ 5/96*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/_
+ (b^4*d)-1/24*(14*a*c+b*c^2/d-63*a^2*d/b)*(c+d*x)^(5/2)*_
+ sqrt(a+b*x)/(b^2*(b*c-a*d))+1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/_
+ (b^2*d)-5/64*(b*c-a*d)*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-------+
+--R (945a d - 2100a b c d + 1350a b c d - 180a b c d - 15b c )\|b x + a
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 4 3 4 3 3 4 2 3
+--R 48b d x + (- 72a b d + 136b c d )x
+--R +
+--R 2 2 3 3 2 4 2 2
+--R (126a b d - 244a b c d + 118b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 4 3
+--R (- 315a b d + 637a b c d - 337a b c d + 15b c )x - 945a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 1785a b c d - 839a b c d + 15a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 5 +-+ +-+ +-------+
+--R 192b d\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 922
+
+--S 923 of 1000
+--a0:=integrate(t0,x)
+--E 923
+
+--S 924 of 1000
+--m0:=a0-r0
+--E 924
+
+--S 925 of 1000
+--d0:=D(m0,x)
+--E 925
+
+)clear all
+
+--S 926 of 1000
+t0:=x*(c+d*x)^(5/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 2 3 2 2 +-------+
+--R (d x + 2c d x + c x)\|d x + c
+--R (1) --------------------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1000
+r0:=5/8*(b*c-7*a*d)*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/(b^(9/2)*sqrt(d))+2*a*(c+d*x)^(7/2)/(b*(b*c-a*d)*_
+ sqrt(a+b*x))+5/12*(b*c-7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b^3+_
+ 1/3*(b*c-7*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*(b*c-a*d))+_
+ 5/8*(b*c-7*a*d)*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^4
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-------+
+--R (- 105a d + 225a b c d - 135a b c d + 15b c )\|b x + a
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 3 2 3 2 2 3 2 2 2 2 3 2
+--R 8b d x + (- 14a b d + 26b c d)x + (35a b d - 68a b c d + 33b c )x
+--R +
+--R 3 2 2 2 2
+--R 105a d - 190a b c d + 81a b c
+--R *
+--R +-+ +-+ +-------+
+--R \|b \|d \|d x + c
+--R /
+--R 4 +-+ +-+ +-------+
+--R 24b \|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1000
+--a0:=integrate(t0,x)
+--E 928
+
+--S 929 of 1000
+--m0:=a0-r0
+--E 929
+
+--S 930 of 1000
+--d0:=D(m0,x)
+--E 930
+
+)clear all
+
+--S 931 of 1000
+t0:=(c+d*x)^(5/2)/(a+b*x)^(3/2)
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R +-------+
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1000
+r0:=15/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
+ sqrt(d)/b^(7/2)-2*(c+d*x)^(5/2)/(b*sqrt(a+b*x))+5/2*d*(c+d*x)^(3/2)*_
+ sqrt(a+b*x)/b^2+15/4*d*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^3
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-+ +-------+ \|d \|b x + a
+--R (15a d - 30a b c d + 15b c )\|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R (2b d x + (- 5a b d + 9b c d)x - 15a d + 25a b c d - 8b c )\|b
+--R *
+--R +-------+
+--R \|d x + c
+--R /
+--R 3 +-+ +-------+
+--R 4b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1000
+--a0:=integrate(t0,x)
+--E 933
+
+--S 934 of 1000
+--m0:=a0-r0
+--E 934
+
+--S 935 of 1000
+--d0:=D(m0,x)
+--E 935
+
+)clear all
+
+--S 936 of 1000
+t0:=(c+d*x)^(5/2)/(x*(a+b*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 2 +-------+
+--R (b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 1000
+r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(3/2)+_
+ d^(3/2)*(5*b*c-3*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
+ sqrt(c+d*x)))/b^(5/2)+2*(c+d*x)^(5/2)/(a*sqrt(a+b*x))-_
+ 2*d*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*b)-d*(2*b*c-3*a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a*b^2)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|d \|b x + a
+--R (- 3a d + 5a b c d)\|a \|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|c \|b x + a
+--R - 2b c \|b \|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 +-+ +-+ +-------+
+--R (a b d x + 3a d - 4a b c d + 2b c )\|a \|b \|d x + c
+--R /
+--R 2 +-+ +-+ +-------+
+--R a b \|a \|b \|b x + a
+--R Type: Expression(Integer)
+--E 937
+
+--S 938 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 938
+
+--S 939 of 1000
+--m0:=a0-r0
+--E 939
+
+--S 940 of 1000
+--d0:=D(m0,x)
+--E 940
+
+)clear all
+
+--S 941 of 1000
+t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 3 2 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1000
+r0:=c^(3/2)*(3*b*c-5*a*d)*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^(3/2)-3*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*_
+ sqrt(a+b*x))-(c+d*x)^(5/2)/(a*x*sqrt(a+b*x))+d*(3*b*c-2*a*d)*_
+ sqrt(a+b*x)*sqrt(c+d*x)/(a^2*b)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|d \|b x + a
+--R 2a d x\|a \|d \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R +-+ +-------+
+--R 2 2 +-+ +-+ +-------+ \|c \|b x + a
+--R (- 5a b c d + 3b c )x\|b \|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 +-+ +-+ +-------+
+--R ((- 2a d + 4a b c d - 3b c )x - a b c )\|a \|b \|d x + c
+--R /
+--R 2 +-+ +-+ +-------+
+--R a b x\|a \|b \|b x + a
+--R Type: Expression(Integer)
+--E 942
+
+--S 943 of 1000 (non-algebraic residues)
+--a0:=integrate(t0,x)
+--E 943
+
+--S 944 of 1000
+--m0:=a0-r0
+--E 944
+
+--S 945 of 1000
+--d0:=D(m0,x)
+--E 945
+
+)clear all
+
+--S 946 of 1000
+t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 4 3 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1000
+r0:=-15/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
+ sqrt(c)/a^(7/2)+5/4*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*x*_
+ sqrt(a+b*x))-1/2*(c+d*x)^(5/2)/(a*x^2*sqrt(a+b*x))+_
+ 15/4*(b*c-a*d)^2*sqrt(c+d*x)/(a^3*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 2 +-+ +-------+ \|c \|b x + a
+--R (- 15a d + 30a b c d - 15b c )x \|c \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 2 2 2 +-+
+--R ((8a d - 25a b c d + 15b c )x + (- 9a c d + 5a b c )x - 2a c )\|a
+--R *
+--R +-------+
+--R \|d x + c
+--R /
+--R 3 2 +-+ +-------+
+--R 4a x \|a \|b x + a
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1000
+--a0:=integrate(t0,x)
+--E 948
+
+--S 949 of 1000
+--m0:=a0-r0
+--E 949
+
+--S 950 of 1000
+--d0:=D(m0,x)
+--E 950
+
+)clear all
+
+--S 951 of 1000
+t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 5 4 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 1000
+r0:=5/8*(b*c-a*d)^2*(7*b*c-a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
+ sqrt(c+d*x)))/(a^(9/2)*sqrt(c))+1/12*(7*b*c-5*a*d)*_
+ (c+d*x)^(3/2)/(a^2*x^2*sqrt(a+b*x))-1/3*(c+d*x)^(5/2)/_
+ (a*x^3*sqrt(a+b*x))-1/24*b*(105*b^2*c^2-190*a*b*c*d+81*a^2*d^2)*_
+ sqrt(c+d*x)/(a^4*sqrt(a+b*x))-1/24*(35*b^2*c^2-54*a*b*c*d+_
+ 15*a^2*d^2)*sqrt(c+d*x)/(a^3*x*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 3 +-------+
+--R (- 15a d + 135a b c d - 225a b c d + 105b c )x \|b x + a
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 3 2 3
+--R (- 81a b d + 190a b c d - 105b c )x
+--R +
+--R 3 2 2 2 2 2 3 2 2 3 2
+--R (- 33a d + 68a b c d - 35a b c )x + (- 26a c d + 14a b c )x - 8a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R /
+--R 4 3 +-+ +-+ +-------+
+--R 24a x \|a \|c \|b x + a
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1000
+--a0:=integrate(t0,x)
+--E 953
+
+--S 954 of 1000
+--m0:=a0-r0
+--E 954
+
+--S 955 of 1000
+--d0:=D(m0,x)
+--E 955
+
+)clear all
+
+--S 956 of 1000
+t0:=(c+d*x)^(5/2)/(x^5*(a+b*x)^(3/2))
+--R
+--R
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|d x + c
+--R (1) ------------------------------
+--R 6 5 +-------+
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1000
+r0:=-5/64*(b*c-a*d)^2*(63*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)*c^(3/2))+_
+ 1/24*(9*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^3*sqrt(a+b*x))-_
+ 1/4*(c+d*x)^(5/2)/(a*x^4*sqrt(a+b*x))+1/192*b*(945*b^3*c^3-_
+ 1785*a*b^2*c^2*d+839*a^2*b*c*d^2-15*a^3*d^3)*sqrt(c+d*x)/_
+ (a^5*c*sqrt(a+b*x))-1/96*(63*b^2*c^2-86*a*b*c*d+15*a^2*d^2)*_
+ sqrt(c+d*x)/(a^3*x^2*sqrt(a+b*x))+1/192*(b*c-a*d)*_
+ (315*b^2*c^2-322*a*b*c*d+15*a^2*d^2)*sqrt(c+d*x)/(a^4*c*x*sqrt(a+b*x))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (15a d + 180a b c d - 1350a b c d + 2100a b c d - 945b c )x
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|b x + a atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 3 2 2 2 3 2 4 3 4
+--R (- 15a b d + 839a b c d - 1785a b c d + 945b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 3
+--R (- 15a d + 337a b c d - 637a b c d + 315a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 118a c d + 244a b c d - 126a b c )x + (- 136a c d + 72a b c )x
+--R +
+--R 4 3
+--R - 48a c
+--R *
+--R +-+ +-+ +-------+
+--R \|a \|c \|d x + c
+--R /
+--R 5 4 +-+ +-+ +-------+
+--R 192a c x \|a \|c \|b x + a
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1000
+--a0:=integrate(t0,x)
+--E 958
+
+--S 959 of 1000
+--m0:=a0-r0
+--E 959
+
+--S 960 of 1000
+--d0:=D(m0,x)
+--E 960
+
+)clear all
+
+--S 961 of 1000
+t0:=x^4/((a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 4
+--R x
+--R (1) -------------------------------------------------
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 1000
+r0:=3/4*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_
+ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+1/2*a*(b*c-5*a*d)*x^2/_
+ (b^2*d*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+1/2*x^3/(b*d*sqrt(a+b*x)*_
+ sqrt(c+d*x))+1/2*c*(4*a*c*(b*c-5*a*d)+(5*b^2*c^2+2*a*b*c*d-_
+ 15*a^2*d^2)*x)*sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^2*sqrt(c+d*x))-_
+ 1/4*(3*b*c-a*d)*(5*b^2*c^2+2*a*b*c*d-15*a^2*d^2)*sqrt(a+b*x)*_
+ sqrt(c+d*x)/(b^3*d^3*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-------+
+--R (15a d - 12a b c d - 6a b c d - 12a b c d + 15b c )\|b x + a
+--R *
+--R +-+ +-------+
+--R +-------+ \|d \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 4 3 3 4 2 2 3
+--R (2a b d - 4a b c d + 2b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 2
+--R (- 5a b d + 5a b c d + 5a b c d - 5b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4 3
+--R (- 15a d + 2a b c d + 10a b c d + 2a b c d - 15b c )x - 15a c d
+--R +
+--R 3 2 2 2 2 3 3 4
+--R 7a b c d + 7a b c d - 15a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 2 3 5 4 4 5 2 3 +-+ +-+ +-------+ +-------+
+--R (4a b d - 8a b c d + 4b c d )\|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1000
+--a0:=integrate(t0,x)
+--E 963
+
+--S 964 of 1000
+--m0:=a0-r0
+--E 964
+
+--S 965 of 1000
+--d0:=D(m0,x)
+--E 965
+
+)clear all
+
+--S 966 of 1000
+t0:=x^3/((a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------------------------------------
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1000
+r0:=-3*(b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
+ (b^(5/2)*d^(5/2))+x^2/(b*d*sqrt(a+b*x)*sqrt(c+d*x))-_
+ a*(4*a*c+3*(b*c+a*d)*x)/(b^2*d*(b*c-a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x))+c*(3*b*c-a*d)*(b*c+a*d)*sqrt(a+b*x)/(b^2*d^2*_
+ (b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-------+ +-------+
+--R (- 3a d + 3a b c d + 3a b c d - 3b c )\|b x + a \|d x + c
+--R *
+--R +-+ +-------+
+--R \|d \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 3 2 2 3 2 2
+--R (a b d - 2a b c d + b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3
+--R (3a d - a b c d - a b c d + 3b c )x + 3a c d - 2a b c d + 3a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R /
+--R 2 2 4 3 3 4 2 2 +-+ +-+ +-------+ +-------+
+--R (a b d - 2a b c d + b c d )\|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1000
+--a0:=integrate(t0,x)
+--E 968
+
+--S 969 of 1000
+--m0:=a0-r0
+--E 969
+
+--S 970 of 1000
+--d0:=D(m0,x)
+--E 970
+
+)clear all
+
+--S 971 of 1000
+t0:=x^2/((a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------------------------------------
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1000
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))-_
+ 2*a^2/(b^2*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))-2*(b^2*c^2+a^2*d^2)*_
+ sqrt(a+b*x)/(b^2*d*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ +-------+ \|d \|b x + a
+--R (2a d - 4a b c d + 2b c )\|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|b \|d x + c
+--R +
+--R 2 2 2 2 2 2 +-+ +-+
+--R ((- 2a d - 2b c )x - 2a c d - 2a b c )\|b \|d
+--R /
+--R 2 3 2 2 3 2 +-+ +-+ +-------+ +-------+
+--R (a b d - 2a b c d + b c d)\|b \|d \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1000
+--a0:=integrate(t0,x)
+--E 973
+
+--S 974 of 1000
+--m0:=a0-r0
+--E 974
+
+--S 975 of 1000
+--d0:=D(m0,x)
+--E 975
+
+)clear all
+
+--S 976 of 1000
+t0:=x/((a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R x
+--R (1) -------------------------------------------------
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1000
+r0:=-2*c/(d*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+2*(b*c+a*d)*sqrt(c+d*x)/_
+ (d*(b*c-a*d)^2*sqrt(a+b*x))
+--R
+--R
+--R (2a d + 2b c)x + 4a c
+--R (2) --------------------------------------------
+--R 2 2 2 2 +-------+ +-------+
+--R (a d - 2a b c d + b c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1000
+--a0:=integrate(t0,x)
+--E 978
+
+--S 979 of 1000
+--m0:=a0-r0
+--E 979
+
+--S 980 of 1000
+--d0:=D(m0,x)
+--E 980
+
+)clear all
+
+--S 981 of 1000
+t0:=1/((a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------
+--R 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1000
+r0:=(-2)/((b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))-4*d*sqrt(a+b*x)/_
+ ((b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R - 4b d x - 2a d - 2b c
+--R (2) --------------------------------------------
+--R 2 2 2 2 +-------+ +-------+
+--R (a d - 2a b c d + b c )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1000 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 +-------+ +-------+
+--R (- 16a b c d x - 8a c d - 8a b c )\|b x + a \|d x + c
+--R +
+--R 2 2 2 2 2 2
+--R ((a b c + 16a b)d + (b c + 16a b c)d)x
+--R +
+--R 2 3 2 2 2 2 3 2 2
+--R ((a c + 16a )d + (2a b c + 32a b c)d + b c + 16a b c )x
+--R +
+--R 2 2 3 3 2 2
+--R (a c + 16a c)d + a b c + 16a b c
+--R /
+--R 3 3 2 2 2 2 3 3 2
+--R (4a b c d - 8a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 2 2 4
+--R (4a c d - 4a b c d - 4a b c d + 4a b c )x + 4a c d - 8a b c d + 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 983
+
+--S 984 of 1000 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R (a c + 16a )d + b c + 16a b c
+--R (4) ------------------------------
+--R 3 2 2 2 2 3
+--R 4a c d - 8a b c d + 4a b c
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1000
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 985
+
+)clear all
+
+--S 986 of 1000
+t0:=1/(x*(a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------
+--R 3 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c x)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1000
+r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(3/2))+_
+ 2*b/(a*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+2*d*(b*c+a*d)*sqrt(a+b*x)/_
+ (a*c*(b*c-a*d)^2*sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 2 2 2 +-------+ +-------+ \|c \|b x + a
+--R (- 2a d + 4a b c d - 2b c )\|b x + a \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 2 2 +-+ +-+
+--R ((2a b d + 2b c d)x + 2a d + 2b c )\|a \|c
+--R /
+--R 3 2 2 2 2 3 +-+ +-+ +-------+ +-------+
+--R (a c d - 2a b c d + a b c )\|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 987
+
+--S 988 of 1000
+--a0:=integrate(t0,x)
+--E 988
+
+--S 989 of 1000
+--m0:=a0-r0
+--E 989
+
+--S 990 of 1000
+--d0:=D(m0,x)
+--E 990
+
+)clear all
+
+--S 991 of 1000
+t0:=1/(x^2*(a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1000
+r0:=3*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
+ (a^(5/2)*c^(5/2))-b*(3*b*c-a*d)/(a^2*c*(b*c-a*d)*sqrt(a+b*x)*_
+ sqrt(c+d*x))+(-1)/(a*c*x*sqrt(a+b*x)*sqrt(c+d*x))-_
+ d*(3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^2*_
+ sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-------+ +-------+
+--R (3a d - 3a b c d - 3a b c d + 3b c )x\|b x + a \|d x + c
+--R *
+--R +-+ +-------+
+--R \|c \|b x + a
+--R atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 3 2 2
+--R (- 3a b d + 2a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3
+--R (- 3a d + a b c d + a b c d - 3b c )x - a c d + 2a b c d - a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 2 2 3 3 2 2 4 +-+ +-+ +-------+ +-------+
+--R (a c d - 2a b c d + a b c )x\|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 992
+
+--S 993 of 1000
+--a0:=integrate(t0,x)
+--E 993
+
+--S 994 of 1000
+--m0:=a0-r0
+--E 994
+
+--S 995 of 1000
+--d0:=D(m0,x)
+--E 995
+
+)clear all
+
+--S 996 of 1000
+t0:=1/(x^3*(a+b*x)^(3/2)*(c+d*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 +-------+ +-------+
+--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1000
+r0:=-3/4*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*sqrt(a+b*x)/_
+ (sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))+1/4*b*(15*b^2*c^2-_
+ 2*a*b*c*d-5*a^2*d^2)/(a^3*c^2*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+_
+ (-1/2)/(a*c*x^2*sqrt(a+b*x)*sqrt(c+d*x))+5/4*(b*c+a*d)/_
+ (a^2*c^2*x*sqrt(a+b*x)*sqrt(c+d*x))+1/4*d*(b*c+a*d)*_
+ (15*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^2*_
+ sqrt(c+d*x))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +-------+
+--R (- 15a d + 12a b c d + 6a b c d + 12a b c d - 15b c )x \|b x + a
+--R *
+--R +-+ +-------+
+--R +-------+ \|c \|b x + a
+--R \|d x + c atanh(--------------)
+--R +-+ +-------+
+--R \|a \|d x + c
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 3
+--R (15a b d - 7a b c d - 7a b c d + 15b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 2
+--R (15a d - 2a b c d - 10a b c d - 2a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3
+--R (5a c d - 5a b c d - 5a b c d + 5a b c )x - 2a c d + 4a b c d
+--R +
+--R 2 2 4
+--R - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 3 2 4 4 3 2 5 2 +-+ +-+ +-------+ +-------+
+--R (4a c d - 8a b c d + 4a b c )x \|a \|c \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 997
+
+--S 998 of 1000
+--a0:=integrate(t0,x)
+--E 998
+
+--S 999 of 1000
+--m0:=a0-r0
+--E 999
+
+--S 1000 of 1000
+--d0:=D(m0,x)
+--E 1000
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3b.input.pdf b/src/axiom-website/CATS/rich3b.input.pdf
new file mode 100644
index 0000000..773f887
Binary files /dev/null and b/src/axiom-website/CATS/rich3b.input.pdf differ
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index f3acf95..e5fec42 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -4248,6 +4248,8 @@ src/axiom-website/CATS/rich1a statistics update
src/axiom-website/CATS/rich1b statistics update
20130725.01.tpd.patch
src/axiom-website/CATS/rich2, rich3a
+20130726.01.tpd.patch
+src/axiom-website/CATS/rich3b