Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.symbolic.independent

Topic: An independent integration test suite
Replies: 128   Last Post: Dec 8, 2013 3:21 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
clicliclic@freenet.de

Posts: 988
Registered: 4/26/08
Re: An independent integration test suite
Posted: Dec 8, 2013 3:21 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


clicliclic@freenet.de schrieb:
>
> [...]
>
> Perhaps other systems (and/or chapters) can be added here by and by.
> I am currently working on chapter 4 (132 integrals) in which I am
> expecially interested, but not expecting to finish this before some
> months have passed. I am not likely to enter the integrals from other
> chapters too (particularly not the remaining massive ones 2, 5, and
> 8).
>


This was written in April. I have now finished the digitization of
Examples from Chapter 4 of Timofeev's book; the algebraic integrals and
model solutions are appended below. Timofeev presents 132 Examples in
Chapter 4, of which the final group (numbers 123 - 132, p. 198-200) are
mere substitution recipes that had to be omitted here. With each Example
consisting of just a single integral, 122 entries result in total.

As in the digitization of other Chapters, nested powers (^r)^(1/s) were
interpreted as ^(r/s), with the exception of Example #1 (just for the
sake of variety). The correction of misprints was straightforward, apart
from Example #53 (p. 164) where the x dependence of the terms in
Timofeev's evaluation corresponds with the integrand denominator, while
their amplitudes are incompatible with the integrand numerator. No
simple correction of integrand and/or antiderivative appears feasible
here, so the integrand was adopted as printed while all the amplitudes
in the antiderivative were changed.

For the default setting of real variables, Derive 6.10 is found to fail
on Examples 13, 15, 17, 20-21, 35, 37-42, 49, 51, 53, 74, 76, 99-100,
107-108, 110, 112-114, and 117-122; additionally it cannot evaluate
Examples 14, 16-21, 23-27, and 46 if the integration variable (and the
occasional parameters) are declared complex.

Timofeev's book can hopefully still be found at:

<h t t p : / / e q w o r l d . i p m n e t . r u / r u / l i b r a r y /
m a t h e m a t i c s / c a l c u l u s . h t m>

The download link being:

<h t t p : / / e q w o r l d . i p m n e t . r u / r u / l i b r a r y /
b o o k s / T i m o f e e v 1 9 4 8 r u . d j v u>

Have fun!

Martin.


" Timofeev (1948) Chapter 4 Integration Examples "

" examples 1 - 10 (p. 115-117) ... "

INT(SQRT(x^3)*(1+x^2)*(2*SQRT(x)-x)^2,x)=x^2*SQRT(x^3)*(8/7-SQRT~
(x)+2/9*x+8/11*x^2-2/3*x^(5/2)+2/13*x^3)

INT((x^(3/2)-3*x^(3/5))^2*(4*x^(3/2)-1/3*x^(2/3)),x)=8/11*x^(11/~
2)-1/14*x^(14/3)-120/23*x^(23/5)+60/113*x^(113/30)+360/37*x^(37/~
10)-45/43*x^(43/15)

INT(1/(1+SQRT(1+x)),x)=2*(SQRT(1+x)-LN(1+SQRT(1+x)))

INT(x/(1+SQRT(1+x)),x)=2/3*(1+x)^(3/2)-x

INT((SQRT(1+x)+1)/(SQRT(1+x)-1),x)=4*LN(SQRT(1+x)-1)+4*SQRT(1+x)~
+x

INT(1/((1+x)^(2/3)-SQRT(1+x)),x)=3*(1+x)^(1/3)+6*(1+x)^(1/6)+6*L~
N((1+x)^(1/6)-1)

INT((1+x^(1/4))^(1/3)/SQRT(x),x)=3/7*(4*SQRT(x)+x^(1/4)-3)*(1+x^~
(1/4))^(1/3)

INT(1/(x^3*(1+x)^(3/2)),x)=(15*x^2+5*x-2)/(4*x^2*SQRT(1+x))-15/4~
*ATANH(1/SQRT(1+x))

INT(1/(x^5*(1-x)^(7/2)),x)=1/(960*x^4*(1-x)^(5/2))*(45045*x^6-10~
5105*x^5+69069*x^4-6435*x^3-1430*x^2-520*x-240)-3003/64*ATANH(1/~
SQRT(1-x))

INT(1/(x^5*(x-1)^(2/3)),x)=(x-1)^(1/3)/(324*x^4)*(220*x^3+132*x^~
2+99*x+81)+55/243*LN((1+(x-1)^(1/3))^3/x)-110/(81*SQRT(3))*ATAN(~
(1-2*(x-1)^(1/3))/SQRT(3))

" examples 11 - 15 (p. 118-120) ... "

INT(SQRT((1-x)/(1+x)),x)=(x+1)*SQRT((1-x)/(x+1))+2*ATAN(1/SQRT((~
1-x)/(x+1)))

INT(SQRT((x-a)/(b-x))*x,x)=1/4*((a-3*b-2*x)*(b-x)*SQRT((x-a)/(b-~
x))+(a+3*b)*(a-b)*ATAN(1/SQRT((x-a)/(b-x))))

INT(SQRT(x-5)*SQRT(x+3)/((x-1)*(x^2-25)),x)=1/(3*SQRT(5))*ATANH(~
SQRT(x-5)/(SQRT(5)*SQRT(x+3)))+1/3*ATAN(SQRT(x-5)/SQRT(x+3))

INT(x^2*(1-x^2)^(1/4)*SQRT(1+x)/(SQRT(1-x)*(SQRT(1-x)-SQRT(1+x))~
),x)=1/48*(1-x)^(1/4)*(1+x)^(1/4)*((8*x^2+22*x+29)*SQRT(1-x)-(8*~
x^2+2*x-7)*SQRT(1+x))-SQRT(2)/8*ATANH(SQRT(2)*(1-x)^(1/4)*(1+x)^~
(1/4)/(SQRT(1-x)+SQRT(1+x)))+3*SQRT(2)/16*ATAN((SQRT(1-x)-SQRT(1~
+x))/(SQRT(2)*(1-x)^(1/4)*(1+x)^(1/4)))=1/48*(1-x)^(1/4)*(1+x)^(~
1/4)*((8*x^2+22*x+29)*SQRT(1-x)-(8*x^2+2*x-7)*SQRT(1+x))-SQRT(2)~
/8*LN(SQRT(1-x)+SQRT(1+x)+SQRT(2)*(1-x)^(1/4)*(1+x)^(1/4))+3*SQR~
T(2)/16*ATAN((SQRT(1-x)-SQRT(1+x))/(SQRT(2)*(1-x)^(1/4)*(1+x)^(1~
/4)))

INT(x*(1+x)^(2/3)*SQRT(1-x)/(SQRT(1+x)*(1-x)^(2/3)-(1+x)^(1/3)*(~
1-x)^(5/6)),x)=-1/12*(1-x)^(1/6)*(3*(3+x)*(1-x)^(5/6)+(10+3*x)*(~
1-x)^(2/3)*(1+x)^(1/6)+(1-3*x)*SQRT(1-x)*(1+x)^(1/3)-3*x*(1-x)^(~
1/3)*SQRT(1+x)-(1+3*x)*(1-x)^(1/6)*(1+x)^(2/3)-(2+3*x)*(1+x)^(5/~
6))+SQRT(3)/18*ATANH(SQRT(3)*(1-x)^(1/6)*(1+x)^(1/6)/((1-x)^(1/3~
)+(1+x)^(1/3)))+1/6*ATAN((1+x)^(1/6)/(1-x)^(1/6))-5/6*ATAN(((1-x~
)^(1/3)-(1+x)^(1/3))/((1-x)^(1/6)*(1+x)^(1/6)))-4*SQRT(3)/9*ATAN~
(((1-x)^(1/3)-2*(1+x)^(1/3))/(SQRT(3)*(1-x)^(1/3)))

" examples 16 - 27 (p. 127-128) ... "

INT(1/((x+1)^2*(x-1)^4)^(1/3),x)=3/2*((x+1)*(1-x)/((x+1)^2*(x-1)~
^4)^(1/3))

INT(1/((x-1)^3*(x+2)^5)^(1/4),x)=4/3*((x-1)*(x+2)/((x-1)^3*(x+2)~
^5)^(1/4))

INT(1/((x+1)^2*(x-1)^7)^(1/3),x)=3/16*((x+1)*(x-1)*(3*x-5)/((x+1~
)^2*(x-1)^7)^(1/3))

INT(1/((x-1)^2*(x+1))^(1/3),x)=(x-1)^(2/3)*(x+1)^(1/3)/((x-1)^2*~
(x+1))^(1/3)*(SQRT(3)*ATAN(((x+1)^(1/3)+2*(x-1)^(1/3))/(SQRT(3)*~
(x+1)^(1/3)))-3/2*LN((x+1)^(1/3)-(x-1)^(1/3)))

INT((x+1/x)*(1/SQRT((x+1)^3*(x-2))),x)=-4*SQRT((x+1)^3*(x-2))/(3~
*(x+1)^2)+2*ATANH(SQRT((x+1)^3*(x-2))/(x+1)^2)+SQRT(2)*ATAN(SQRT~
((x+1)^3*(x-2))/(SQRT(2)*(x+1)^2))

INT(((x-1)^2*(x+1))^(1/3)/x^2,x)=-((x-1)^2*(x+1))^(1/3)/x+((x-1)~
^2*(x+1))^(1/3)/((x-1)^(2/3)*(x+1)^(1/3))*(1/6*LN(x)-1/2*LN((x+1~
)^(1/3)+(x-1)^(1/3))-3/2*LN((x+1)^(1/3)-(x-1)^(1/3))-1/SQRT(3)*A~
TAN(((x+1)^(1/3)-2*(x-1)^(1/3))/(SQRT(3)*(x+1)^(1/3)))-SQRT(3)*A~
TAN(((x+1)^(1/3)+2*(x-1)^(1/3))/(SQRT(3)*(x+1)^(1/3))))

INT(1/(x^2-2*x-3)^(5/2),x)=(x-1)*(x^2-2*x-5)/(24*(x^2-2*x-3)^(3/~
2))

INT(1/SQRT(x^3-5*x^2+3*x+9),x)=-ATANH(SQRT(x^3-5*x^2+3*x+9)/(2*(~
x-3)))

INT(1/(x^3-5*x^2+3*x+9)^(3/2),x)=(15*x^2-70*x+43)/(256*(x-3)*SQR~
T(x^3-5*x^2+3*x+9))-15/512*ATANH(SQRT(x^3-5*x^2+3*x+9)/(2*(x-3)))

INT(1/(x^3-5*x^2+3*x+9)^(1/3),x)=(x+1)^(1/3)*(x-3)^(2/3)/(x^3-5*~
x^2+3*x+9)^(1/3)*(SQRT(3)*ATAN(((x+1)^(1/3)+2*(x-3)^(1/3))/(SQRT~
(3)*(x+1)^(1/3)))-3/2*LN((x+1)^(1/3)-(x-3)^(1/3)))

INT(1/(x^3-5*x^2+3*x+9)^(2/3),x)=-3*(x^3-5*x^2+3*x+9)^(1/3)/(4*(~
x-3))

INT(1/(x^3-5*x^2+3*x+9)^(4/3),x)=3*(9*x^2-42*x+29)/(320*(x-3)*(x~
^3-5*x^2+3*x+9)^(1/3))

" examples 28 - 42 (p. 143-146) ... "

INT(1/SQRT(4+3*x-2*x^2),x)=1/SQRT(2)*ASIN((4*x-3)/SQRT(41))

INT(1/SQRT(-3+4*x-x^2),x)=ASIN(x-2)

INT(1/SQRT(-2-5*x-3*x^2),x)=1/SQRT(3)*ASIN(6*x+5)

INT(1/((x^2+4)*SQRT(1-x^2)),x)=SQRT(5)/10*ATAN(SQRT(5)*x/(2*SQRT~
(1-x^2)))

INT(1/((x^2+4)*SQRT(4*x^2+1)),x)=SQRT(15)/30*ATANH(SQRT(15)*x/(2~
*SQRT(4*x^2+1)))

INT(x/((3-x^2)*SQRT(5-x^2)),x)=1/SQRT(2)*ATANH(SQRT(2)/SQRT(5-x^~
2))

INT(x/((5-x^2)*SQRT(3-x^2)),x)=-1/SQRT(2)*ATAN(SQRT(3-x^2)/SQRT(~
2))

INT(1/((x^4-1)*SQRT(x^2+2)),x)=-SQRT(3)/6*ATANH(SQRT(3)*x/SQRT(x~
^2+2))-1/2*ATAN(x/SQRT(x^2+2))

INT(x/((x^2-1)*SQRT(x^2+2*x+4)),x)=-SQRT(3)/6*ATANH(SQRT(3)/SQRT~
(x^2+2*x+4))-SQRT(7)/14*ATANH((2*x+5)/(SQRT(7)*SQRT(x^2+2*x+4)))

INT(1/((x^3-8)*SQRT(x^2+2*x+5)),x)=1/12*ATANH(1/SQRT(x^2+2*x+5))~
-1/(12*SQRT(13))*ATANH((7+3*x)/(SQRT(13)*SQRT(x^2+2*x+5)))-SQRT(~
3)/12*ATAN((x+1)/(SQRT(3)*SQRT(x^2+2*x+5)))

INT(x/((x^2+x+4)*SQRT(4*x^2+4*x+5)),x)=-1/SQRT(165)*ATANH(SQRT(1~
1)*(2*x+1)/(SQRT(15)*SQRT(4*x^2+4*x+5)))-1/SQRT(11)*ATAN(SQRT(11~
)/SQRT(4*x^2+4*x+5))

INT((x+3)/((x^2+1)*SQRT(x^2+x+1)),x)=SQRT(2)*ATANH((1+x)/(SQRT(2~
)*SQRT(x^2+x+1)))-2*SQRT(2)*ATAN((1-x)/(SQRT(2)*SQRT(x^2+x+1)))

INT((2*x+1)/((3*x^2+4*x+4)*SQRT(x^2+6*x-1)),x)=-1/(3*SQRT(7))*AC~
OTH(SQRT(7)*(1+x)/SQRT(x^2+6*x-1))-5/(6*SQRT(14))*ATAN(SQRT(7)*(~
2-x)/(SQRT(8)*SQRT(x^2+6*x-1)))

INT((a*x+b)/((5*x^2-18*x+17)*SQRT(10*x^2-22*x+13)),x)=(a+b)/(2*S~
QRT(35))*ATANH(SQRT(35)*(x-1)/(2*SQRT(10*x^2-22*x+13)))-(2*a+b)/~
SQRT(35)*ATAN(SQRT(35)*(2-x)/SQRT(10*x^2-22*x+13))

INT((x-2)/((5*x^2-18*x+17)*SQRT(10*x^2-22*x+13)),x)=-1/(2*SQRT(3~
5))*ATANH(SQRT(35)*(x-1)/(2*SQRT(10*x^2-22*x+13)))

" examples 43 - 84 (p. 163-167) ... "

INT(x^4*SQRT(5-x^2),x)=x/48*(8*x^4-10*x^2-75)*SQRT(5-x^2)+125/16~
*ASIN(x/SQRT(5))

INT(1/(x^6*SQRT(x^2+2)),x)=-(3-2*x^2+2*x^4)/(30*x^5)*SQRT(x^2+2)

INT(1/(2*x^2+3)^(7/2),x)=x*(32*x^4+120*x^2+135)/(405*(2*x^2+3)^(~
5/2))

INT(x/(1+x^2+a*SQRT(1+x^2)),x)=LN(a+SQRT(1+x^2))

INT((x^2-x+1)/((1+x^2)*SQRT(1+x^2)),x)=1/SQRT(1+x^2)+ATANH(x/SQR~
T(1+x^2))=1/SQRT(1+x^2)+LN(x+SQRT(1+x^2))

INT(SQRT(1+x^2)/(2+x^2),x)=ATANH(x/SQRT(1+x^2))-SQRT(2)/2*ATANH(~
x/(SQRT(2)*SQRT(1+x^2)))=LN(x+SQRT(1+x^2))-SQRT(2)/2*ATANH(x/(SQ~
RT(2)*SQRT(1+x^2)))

INT(1/((2+x^2)^2*SQRT(1+x^2)),x)=-x*SQRT(1+x^2)/(4*(2+x^2))+3/(4~
*SQRT(2))*ATANH(x/(SQRT(2)*SQRT(1+x^2)))

INT(x^2/((x^2-6)*SQRT(x^2-2)),x)=ACOTH(x/SQRT(x^2-2))-SQRT(6)/2*~
ACOTH(SQRT(2)*x/(SQRT(3)*SQRT(x^2-2)))=LN(x+SQRT(x^2-2))-SQRT(6)~
/2*ACOTH(SQRT(2)*x/(SQRT(3)*SQRT(x^2-2)))

INT((x^2+5)/((1+x^2)^2*SQRT(1-x^2)),x)=x*SQRT(1-x^2)/(1+x^2)+2*S~
QRT(2)*ATAN(SQRT(2)*x/SQRT(1-x^2))

INT((4*x-SQRT(1-x^2))/(5+SQRT(1-x^2)),x)=-x-4*SQRT(1-x^2)+20*LN(~
5+SQRT(1-x^2))-25/(2*SQRT(6))*ATAN(2*SQRT(6)*x/(1+5*SQRT(1-x^2))~
)+5*ASIN(x)

INT((2-SQRT(x^2+1))*x^2/(SQRT(x^2+1)*((x^2+1)^(3/2)-x^3+1)),x)=(~
16-3*x)/18*(x+SQRT(x^2+1))-7/54*LN(3*x^2+2*x+3)-41/54*ATANH(x/SQ~
RT(x^2+1))-7/27*ATANH((x-1)/(2*SQRT(x^2+1)))+4*SQRT(2)/27*ATAN((~
3*x+1)/SQRT(8))+4*SQRT(2)/27*ATAN((x+1)/(SQRT(2)*SQRT(x^2+1)))=(~
16-3*x)/18*(x+SQRT(x^2+1))-7/54*LN(3*x^2+2*x+3)-41/54*LN(x+SQRT(~
x^2+1))-7/27*ATANH((x-1)/(2*SQRT(x^2+1)))+4*SQRT(2)/27*ATAN((3*x~
+1)/SQRT(8))+4*SQRT(2)/27*ATAN((x+1)/(SQRT(2)*SQRT(x^2+1)))

INT(x*SQRT(2*r*x-x^2),x)=(2*x^2-r*x-3*r^2)/6*SQRT(2*r*x-x^2)+1/2~
*r^3*ATAN((x-r)/SQRT(2*r*x-x^2))

INT(x^2*SQRT(2*r*x-x^2),x)=(6*x^3-2*r*x^2-5*r^2*x-15*r^3)/24*SQR~
T(2*r*x-x^2)+5/8*r^4*ATAN((x-r)/SQRT(2*r*x-x^2))

INT(x^3*SQRT(2*r*x-x^2),x)=(24*x^4-6*r*x^3-14*r^2*x^2-35*r^3*x-1~
05*r^4)/120*SQRT(2*r*x-x^2)+7/8*r^5*ATAN((x-r)/SQRT(2*r*x-x^2))

INT(1/((x^2-1)*SQRT(2*x+x^2)),x)=-SQRT(3)/6*ACOTH((1+2*x)/(SQRT(~
3)*SQRT(2*x+x^2)))-1/2*ATAN(SQRT(2*x+x^2))

INT((3*x-2)/((x+1)^3*SQRT(2*x-x^2)),x)=-(4*x+9)/(6*(x+1)^2)*SQRT~
(2*x-x^2)-SQRT(3)/6*ATAN((2*x-1)/(SQRT(3)*SQRT(2*x-x^2)))

INT(1/SQRT(1+x+x^2),x)=ATANH((1+2*x)/(2*SQRT(1+x+x^2)))=LN(1+2*x~
+2*SQRT(1+x+x^2))

INT(x^3/SQRT(1+x+x^2),x)=(8*x^2-10*x-1)/24*SQRT(1+x+x^2)+7/16*AT~
ANH((1+2*x)/(2*SQRT(1+x+x^2)))=(8*x^2-10*x-1)/24*SQRT(1+x+x^2)+7~
/16*LN(1+2*x+2*SQRT(1+x+x^2))

INT(1/(1+x+x^2)^(3/2),x)=2*(2*x+1)/(3*SQRT(1+x+x^2))

INT(x/(1+x+x^2)^(3/2),x)=-2*(x+2)/(3*SQRT(1+x+x^2))

INT(x^3/(1+x+x^2)^(3/2),x)=(3*x^2+7*x+5)/(3*SQRT(1+x+x^2))-3/2*A~
TANH((1+2*x)/(2*SQRT(1+x+x^2)))=(3*x^2+7*x+5)/(3*SQRT(1+x+x^2))-~
3/2*LN(1+2*x+2*SQRT(1+x+x^2))

INT(x^2*SQRT(1+x+x^2),x)=(48*x^3+8*x^2+14*x-37)/192*SQRT(1+x+x^2~
)+3/128*ATANH((1+2*x)/(2*SQRT(1+x+x^2)))=(48*x^3+8*x^2+14*x-37)/~
192*SQRT(1+x+x^2)+3/128*LN(1+2*x+2*SQRT(1+x+x^2))

INT((1+x+x^2)^(3/2),x)=(2*x+1)*(8*x^2+8*x+17)/64*SQRT(1+x+x^2)+2~
7/128*ATANH((1+2*x)/(2*SQRT(1+x+x^2)))=(2*x+1)*(8*x^2+8*x+17)/64~
*SQRT(1+x+x^2)+27/128*LN(1+2*x+2*SQRT(1+x+x^2))

INT((1+x+x^2)^(5/2),x)=(2*x+1)*(128*x^4+256*x^3+504*x^2+376*x+38~
3)/1536*SQRT(1+x+x^2)+135/1024*ATANH((1+2*x)/(2*SQRT(1+x+x^2)))=~
(2*x+1)*(128*x^4+256*x^3+504*x^2+376*x+383)/1536*SQRT(1+x+x^2)+1~
35/1024*LN(1+2*x+2*SQRT(1+x+x^2))

INT(1/(x^2*SQRT(1+x+x^2)),x)=-SQRT(1+x+x^2)/x+1/2*ATANH((2+x)/(2~
*SQRT(1+x+x^2)))

INT(1/(x^3*SQRT(1+x+x^2)),x)=(3*x-2)/(4*x^2)*SQRT(1+x+x^2)+1/8*A~
TANH((2+x)/(2*SQRT(1+x+x^2)))

INT(1/(x^2*(1+x+x^2)^(3/2)),x)=-(5*x^2+7*x+3)/(3*x*SQRT(1+x+x^2)~
)+3/2*ATANH((2+x)/(2*SQRT(1+x+x^2)))

INT(1/(x^3*(1+x+x^2)^(3/2)),x)=(37*x^3+23*x^2+15*x-6)/(12*x^2*SQ~
RT(1+x+x^2))-3/8*ATANH((2+x)/(2*SQRT(1+x+x^2)))

INT(1/((x+1)*SQRT(1+x+x^2)),x)=ATANH((x-1)/(2*SQRT(x^2+x+1)))

INT(1/((x^3-x)*SQRT(x^2+2*x+4)),x)=1/2*ATANH((x+4)/(2*SQRT(x^2+2~
*x+4)))-SQRT(7)/14*ATANH((2*x+5)/(SQRT(7)*SQRT(x^2+2*x+4)))-SQRT~
(3)/6*ATANH(SQRT(3)/SQRT(x^2+2*x+4))

INT(SQRT(x^2+2*x+4)/(x-1)^2,x)=SQRT(x^2+2*x+4)/(1-x)+ATANH((x+1)~
/SQRT(x^2+2*x+4))-2/SQRT(7)*ATANH((2*x+5)/(SQRT(7)*SQRT(x^2+2*x+~
4)))=SQRT(x^2+2*x+4)/(1-x)+LN(x+1+SQRT(x^2+2*x+4))-2/SQRT(7)*ATA~
NH((2*x+5)/(SQRT(7)*SQRT(x^2+2*x+4)))

INT((2*x+3)/((x^2+2*x+3)^2*SQRT(x^2+2*x+4)),x)=(x-3)/(4*(x^2+2*x~
+3))*SQRT(x^2+2*x+4)+ATANH(1/SQRT(x^2+2*x+4))-SQRT(2)/8*ATAN((x+~
1)/(SQRT(2)*SQRT(x^2+2*x+4)))

INT((2*x^3+3*x^2)/((2*x^2+x-3)*SQRT(x^2+2*x-3)),x)=(2*x-3)/(2*(x~
-1))*SQRT(x^2+2*x-3)

INT((x^4+1)/((x^2+x+1)*SQRT(x^2+x+2)),x)=(2*x-7)/4*SQRT(x^2+x+2)~
-1/8*ATANH((2*x+1)/(2*SQRT(x^2+x+2)))-ATANH(1/SQRT(x^2+x+2))+1/S~
QRT(3)*ATAN((2*x+1)/(SQRT(3)*SQRT(x^2+x+2)))=(2*x-7)/4*SQRT(x^2+~
x+2)-1/8*LN(2*x+1+2*SQRT(x^2+x+2))-ATANH(1/SQRT(x^2+x+2))+1/SQRT~
(3)*ATAN((2*x+1)/(SQRT(3)*SQRT(x^2+x+2)))

INT(1/(x^2+2*x+4)^(7/2),x)=(x+1)*(8*x^4+32*x^3+108*x^2+152*x+203~
)/(405*(x^2+2*x+4)^(5/2))

INT(1/(3*x^2+8*x+1)^(5/2),x)=(3*x+4)*(18*x^2+48*x-7)/(507*(3*x^2~
+8*x+1)^(3/2))

INT(1/(5+4*x-3*x^2)^(5/2),x)=(3*x-2)*(49+24*x-18*x^2)/(1083*(5+4~
*x-3*x^2)^(3/2))

INT(1/(1+SQRT(x^2+2*x+2)),x)=(1-SQRT(x^2+2*x+2))/(x+1)+ATANH((x+~
1)/SQRT(x^2+2*x+2))=(1-SQRT(x^2+2*x+2))/(x+1)+LN(x+1+SQRT(x^2+2*~
x+2))

INT(1/(x+SQRT(1+x+x^2)),x)=SQRT(1+x+x^2)-x+LN(x-1+2*SQRT(1+x+x^2~
))-1/2*ATANH((2*x+1)/(2*SQRT(1+x+x^2)))=SQRT(1+x+x^2)-x+LN(x-1+2~
*SQRT(1+x+x^2))-1/2*LN(2*x+1+2*SQRT(1+x+x^2))

INT(x^2/(2*x+1+2*SQRT(1+x+x^2)),x)=(48*x^3+8*x^2+14*x-37)/288*SQ~
RT(1+x+x^2)-x^3*(3*x+2)/18+1/64*ATANH((2*x+1)/(2*SQRT(1+x+x^2)))~
=(48*x^3+8*x^2+14*x-37)/288*SQRT(1+x+x^2)-x^3*(3*x+2)/18+1/64*LN~
(2*x+1+2*SQRT(1+x+x^2))

INT((SQRT(1+x+x^2)-3*x)/(SQRT(1+x+x^2)-1),x)=x-3*SQRT(1+x+x^2)+L~
N(2*SQRT(1+x+x^2)-2-x)-4*LN(2*SQRT(1+x+x^2)-1+x)+5/2*ATANH((2*x+~
1)/(2*SQRT(1+x+x^2)))=x-3*SQRT(1+x+x^2)+LN(2*SQRT(1+x+x^2)-2-x)-~
4*LN(2*SQRT(1+x+x^2)-1+x)+5/2*LN(1+2*x+2*SQRT(1+x+x^2))

INT((x+1)/(SQRT(x^2+2*x+4)-SQRT(x^2+x+1)),x)=(x-3)/2*SQRT(x^2+2*~
x+4)+(2*x-7)/4*SQRT(x^2+x+1)-2*SQRT(7)*LN(2*x-1+SQRT(7)*SQRT(x^2~
+2*x+4))+2*SQRT(7)*LN(2*SQRT(7)*SQRT(x^2+x+1)-5*x-1)+11/2*ATANH(~
(x+1)/SQRT(x^2+2*x+4))+43/8*ATANH((2*x+1)/(2*SQRT(x^2+x+1)))=(x-~
3)/2*SQRT(x^2+2*x+4)+(2*x-7)/4*SQRT(x^2+x+1)-2*SQRT(7)*LN(2*x-1+~
SQRT(7)*SQRT(x^2+2*x+4))+2*SQRT(7)*LN(2*SQRT(7)*SQRT(x^2+x+1)-5*~
x-1)+11/2*LN(x+1+SQRT(x^2+2*x+4))+43/8*LN(2*x+1+2*SQRT(x^2+x+1))

" examples 85 - 100 (p. 177-178) ... "

INT(1/(x^3*SQRT(x-1)),x)=(3*x+2)*SQRT(x-1)/(4*x^2)+3/4*ATAN(SQRT~
(x-1))

INT(1/(x^2*(1-3/x)^(4/3)),x)=-1/(1-3/x)^(1/3)

INT((3*x-1)^(4/3)/x^2,x)=(9*x+1)*(3*x-1)^(1/3)/x+2*LN(x)-6*LN((3~
*x-1)^(1/3)+1)-4*SQRT(3)*ATAN((2*(3*x-1)^(1/3)-1)/SQRT(3))

INT((4-3*x)^(4/3)*x^2,x)=-(35*x^2+28*x+16)/455*(4-3*x)^(7/3)

INT((1-2*x^(1/3))^(3/4)/x,x)=4*(1-2*x^(1/3))^(3/4)-6*ATANH((1-2*~
x^(1/3))^(1/4))+6*ATAN((1-2*x^(1/3))^(1/4))

INT(x/(3-2*SQRT(x))^(3/4),x)=-4/65*(5*x^(3/2)+10*x+24*SQRT(x)+14~
4)*(3-2*SQRT(x))^(1/4)

INT((2*SQRT(x)-1)^(5/4)/x^2,x)=(2-9*SQRT(x))*(2*SQRT(x)-1)^(1/4)~
/(2*x)+5*SQRT(2)/4*ATANH(SQRT(2)*(2*SQRT(x)-1)^(1/4)/(1+SQRT(2*S~
QRT(x)-1)))-5*SQRT(2)/4*ATAN((1-SQRT(2*SQRT(x)-1))/(SQRT(2)*(2*S~
QRT(x)-1)^(1/4)))

INT((x^7+1)^(1/3)*x^6,x)=3/28*(x^7+1)^(4/3)

INT(x^6/(x^7+1)^(5/3),x)=-3/(14*(x^7+1)^(2/3))

INT(1/(x*(2*x^7-27)^(2/3)),x)=1/42*LN((2*x^7-27)^(1/3)+3)-1/18*L~
N(x)+SQRT(3)/63*ATAN((2*(2*x^7-27)^(1/3)-3)/(3*SQRT(3)))

INT((x^7+1)^(2/3)/x^8,x)=-(x^7+1)^(2/3)/(7*x^7)+1/7*LN((x^7+1)^(~
1/3)-1)-1/3*LN(x)+2*SQRT(3)/21*ATAN((2*(x^7+1)^(1/3)+1)/SQRT(3))

INT((3+4*x^4)^(1/4)/x^2,x)=-(3+4*x^4)^(1/4)/x+1/SQRT(2)*ATANH(SQ~
RT(2)*x/(3+4*x^4)^(1/4))-1/SQRT(2)*ATAN(SQRT(2)*x/(3+4*x^4)^(1/4~
))

INT(x^2*(3+4*x^4)^(5/4),x)=x^3*(16*x^4+27)*(3+4*x^4)^(1/4)/32+45~
*SQRT(2)/256*ATANH(SQRT(2)*x/(3+4*x^4)^(1/4))-45*SQRT(2)/256*ATA~
N(SQRT(2)*x/(3+4*x^4)^(1/4))

INT(x^6*(3+4*x^4)^(1/4),x)=x^3*(16*x^4+3)*(3+4*x^4)^(1/4)/128-27~
*SQRT(2)/1024*ATANH(SQRT(2)*x/(3+4*x^4)^(1/4))+27*SQRT(2)/1024*A~
TAN(SQRT(2)*x/(3+4*x^4)^(1/4))

INT((x*(1-x^2))^(1/3),x)=x/2*(x*(1-x^2))^(1/3)-(x*(1-x^2))^(1/3)~
/(x^(1/3)*(1-x^2)^(1/3))*(1/4*LN(x^(2/3)+(1-x^2)^(1/3))+SQRT(3)/~
6*ATAN(((1-x^2)^(1/3)-2*x^(2/3))/(SQRT(3)*(1-x^2)^(1/3))))

INT(SQRT(x*(1+x^(1/3))),x)=(384*x^(4/3)+48*x-56*x^(2/3)+70*x^(1/~
3)-105)/(640*x^(1/3))*SQRT(x*(1+x^(1/3)))+21/128*ATANH(x^(2/3)/S~
QRT(x*(1+x^(1/3))))

" examples 101 - 122 (p. 193-196) ... "

INT(x^3/((x^4-1)*SQRT(2*x^8+1)),x)=-1/(4*SQRT(3))*ATANH((2*x^4+1~
)/(SQRT(3)*SQRT(2*x^8+1)))

INT(x^9*SQRT(1+x^5+x^10),x)=(5+2*x^5+8*x^10)/120*SQRT(1+x^5+x^10~
)-3/80*ATANH((1+2*x^5)/(2*SQRT(1+x^5+x^10)))=(5+2*x^5+8*x^10)/12~
0*SQRT(1+x^5+x^10)-3/80*LN(1+2*x^5+2*SQRT(1+x^5+x^10))

INT(1/(x^5*SQRT(4+2*x^2+x^4)),x)=(3*x^2-4)/(64*x^4)*SQRT(4+2*x^2~
+x^4)+1/128*ATANH((x^2+4)/(2*SQRT(4+2*x^2+x^4)))

INT((x^2-1)/(x*SQRT(1+3*x^2+x^4)),x)=ATANH((1+x^2)/SQRT(1+3*x^2+~
x^4))

INT((x^4-3*x^2)^(3/5)*(2*x^3-3*x),x)=5/16*(x^4-3*x^2)^(8/5)

INT((3*x^8-2*x^5-x^2*(3*x^3-1)^(2/3))/(3*x^3-1)^(3/4),x)=4/243*(~
3*x^3-1)^(9/4)-4/33*(3*x^3-1)^(11/12)-4/27*(3*x^3-1)^(1/4)

INT(1/((x^3-1)*(x^3+2)^(1/3)),x)=1/(2*3^(1/3))*LN(3^(1/3)*x-(x^3~
+2)^(1/3))-1/(6*3^(1/3))*LN(x^3-1)-1/(SQRT(3)*3^(1/3))*ATAN(((x^~
3+2)^(1/3)+2*3^(1/3)*x)/(SQRT(3)*(x^3+2)^(1/3)))

INT(1/((x^4+1)*(x^4+2)^(1/4)),x)=1/(2*SQRT(2))*ATANH(SQRT(2)*x*(~
x^4+2)^(1/4)/(x^2+SQRT(x^4+2)))-1/(2*SQRT(2))*ATAN(SQRT(2)*x*(x^~
4+2)^(1/4)/(x^2-SQRT(x^4+2)))

INT((x^3-1)/(x^3+2)^(1/3),x)=x/3*(x^3+2)^(2/3)+5/6*LN((x^3+2)^(1~
/3)-x)-5/(3*SQRT(3))*ATAN(((x^3+2)^(1/3)+2*x)/(SQRT(3)*(x^3+2)^(~
1/3)))

INT((x^4+1)^(3/4)/(x^4+2)^2,x)=x/(8*(x^4+2))*(x^4+1)^(3/4)+3/(16~
*8^(1/4))*ATANH(x/(2^(1/4)*(x^4+1)^(1/4)))+3/(16*8^(1/4))*ATAN(x~
/(2^(1/4)*(x^4+1)^(1/4)))

INT((x^5-2)^2/((x^5+3)^3*(x^5+3)^(1/5)),x)=x*(97*x^10+462*x^5+11~
88)/(891*(x^5+3)^(11/5))

INT(1/((x^3+3*x^2+3*x)*(x^3+3*x^2+3*x+3)^(1/3)),x)=1/(2*3^(1/3))~
*LN(3^(1/3)*(x+1)-(x^3+3*x^2+3*x+3)^(1/3))-1/(2*3^(4/3))*LN(x^3+~
3*x^2+3*x)-1/3^(5/6)*ATAN(((x^3+3*x^2+3*x+3)^(1/3)+2*3^(1/3)*(x+~
1))/(SQRT(3)*(x^3+3*x^2+3*x+3)^(1/3)))

INT((1-x^2)/((1+x^2)*SQRT(1+x^4)),x)=1/SQRT(2)*ATAN(SQRT(2)*x/SQ~
RT(1+x^4))

INT((1+x^2)/((1-x^2)*SQRT(1+x^4)),x)=1/SQRT(2)*ATANH(SQRT(2)*x/S~
QRT(1+x^4))

INT((x^2+1)/(x*SQRT(1+x^4)),x)=ATANH((x^2-1)/SQRT(1+x^4))

INT((x^2-1)/(x*SQRT(1+x^4)),x)=ATANH((x^2+1)/SQRT(1+x^4))

INT((1+x^2)/((1-x^2)*SQRT(1+x^2+x^4)),x)=1/SQRT(3)*ATANH(SQRT(3)~
*x/SQRT(1+x^2+x^4))

INT((1-x^2)/((1+x^2)*SQRT(1+x^2+x^4)),x)=ATAN(x/SQRT(1+x^2+x^4))

INT((x^4-1)/(x^2*SQRT(x^4+x^2+1)),x)=SQRT(x^4+x^2+1)/x

INT((1-x^2)/((1+2*a*x+x^2)*SQRT(1+2*a*x+2*b*x^2+2*a*x^3+x^4)),x)~
=1/SQRT(2*(1-b))*ATAN((a+2*(a^2-b+1)*x+a*x^2)/(SQRT(2*(1-b))*SQR~
T(1+2*a*x+2*b*x^2+2*a*x^3+x^4)))

INT(1/((1+x^4)*SQRT(SQRT(1+x^4)-x^2)),x)=ATAN(x/SQRT(SQRT(1+x^4)~
-x^2))

INT(1/((1+x^(2*n))*SQRT((1+x^(2*n))^(1/n)-x^2)),x)=ATAN(x/SQRT((~
1+x^(2*n))^(1/n)-x^2))

" ... end of Timofeev Chapter 4 "


Date Subject Author
2/24/13
Read An independent integration test suite
clicliclic@freenet.de
3/19/13
Read where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/21/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/22/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/26/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/26/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Nasser Abbasi
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/21/13
Read Re: An independent integration test suite
Waldek Hebisch
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/22/13
Read Re: An independent integration test suite
Axel Vogt
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/23/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
Richard Fateman
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Richard Fateman
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Axel Vogt
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/25/13
Read Re: An independent integration test suite
Peter Pein
4/25/13
Read Re: An independent integration test suite
Nasser Abbasi
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Richard Fateman
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Richard Fateman
6/30/13
Read Re: An independent integration test suite
clicliclic@freenet.de
6/30/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite / Chap 3
clicliclic@freenet.de
7/1/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite
Waldek Hebisch
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/5/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/5/13
Read Re: An independent integration test suite
Nasser Abbasi
7/9/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/10/13
Read Re: An independent integration test suite
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite/ Klerer?
Richard Fateman
7/10/13
Read Re: An independent integration test suite/ Klerer?
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite
clicliclic@freenet.de
8/6/13
Read Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/24/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/30/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/26/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/29/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
10/1/13
Read The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
10/11/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/22/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Richard Fateman
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Waldek Hebisch
4/21/13
Read Re: An independent integration test suite
G. A. Edgar
12/8/13
Read Re: An independent integration test suite
clicliclic@freenet.de
10/5/13
Read Re: An independent integration test suite
Albert D. Rich
10/6/13
Read Re: An independent integration test suite
clicliclic@freenet.de

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.