error in antiderivative of rational function

[Gui]

Hello everybody,

Maple anwsers something obviously false when asking him the
antiderivative of an innocent-looking fraction. Any explanation ????

icj4 ~ $ maple
|\^/| Maple 15 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple
Inc. 2011
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> int(x^5/((x^3+1)*(x^3+8)),x);
2 5 2
1/6 ln(x ) + 1/3 ln(x + 9 x )

Thanks in advance,
Guillaume

[Nasser M. Abbasi]

In V17, Maple got it right:

int(x^5/((x^3+1)*(x^3+8)),x);

-(1/21)*ln(x+1)+(8/21)*ln(x+2)-(1/21)*ln(x^2-x+1)+(8/21)*ln(x^2-2*x+4)

M V9.01 gives a simpler expression. They are equiveleant

In[68]:= mma = Integrate[x^5/((x^3 + 1) (x^3 + 8)), x]
Out[68]= -(1/21) Log[1 + x^3] + 8/21 Log[8 + x^3]

--Nasser

[Axel Vogt]

restart; interface(version);

Classic Worksheet Interface, Maple 15.01, Windows, Jun 1 2011, Build ID 635520


f:=x^5/((x^3+1)*(x^3+8));
F:=int(f,x);

F := 8/21*ln(x+2)-1/21*ln(x^2-x+1)+8/21*ln(x^2-2*x+4)-1/21*ln(x+1)


f - diff(F, x);
simplify(%);

0

However F is not continous, just plot it

plot([Re(F), Im(F)]);

[G. A. Edgar]

In article <atcqob...@mid.individual.net>, Axel Vogt

> [...]

Maple 15 on Mac also has the correct answer. Is this one of those
Linus-only bugs?

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

[John Harper]

Possibly in Maple 15, but Maple 16 (X86 64 LINUX) gets it right.

--
John Harper

[acer]

Interesting.

What's the value of `libname`, and are there are any unusual .mla or .m files in it?

Here's what I get, using 15.00 and 15.01.

|\^/| Maple 15 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2011
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> int(x^5/((x^3+1)*(x^3+8)),x);

2 2
-1/21 ln(x - x + 1) + 8/21 ln(x - 2 x + 4) + 8/21 ln(x + 2) - 1/21 ln(x + 1)

> kernelopts(version);
Maple 15.00, X86 64 LINUX, Mar 20 2011, Build ID 582305

|\^/| Maple 15 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2011
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> int(x^5/((x^3+1)*(x^3+8)),x);

2 2
-1/21 ln(x - x + 1) - 1/21 ln(x + 1) + 8/21 ln(x - 2 x + 4) + 8/21 ln(x + 2)

> kernelopts(version);
Maple 15.01, X86 64 LINUX, Jun 1 2011, Build ID 635833

[guillaum...@gmail.com]

Le mercredi 24 avril 2013 09:59:14 UTC+2, acer a écrit :

> What's the value of `libname`, and are there are any unusual .mla or .m files > > in it?

libname = /usr/local/maple15/lib

doesn't seem to contain anything unusual.

/usr/local/maple15/lib/units.mla
/usr/local/maple15/lib/Student.mla
/usr/local/maple15/lib/Statistics.mla
/usr/local/maple15/lib/scandsea.mla
/usr/local/maple15/lib/Physics.mla
/usr/local/maple15/lib/Optimization.mla
/usr/local/maple15/lib/MmaTranslator.mla
/usr/local/maple15/lib/Maplets.mla
/usr/local/maple15/lib/MapleToolboxForMatlab.mla
/usr/local/maple15/lib/maple.mla
/usr/local/maple15/lib/InstallerBuilder.mla
/usr/local/maple15/lib/Finance.mla
/usr/local/maple15/lib/DifferentialGeometry.mla
/usr/local/maple15/lib/ContextMenu.mla
/usr/local/maple15/lib/CodeGeneration.mla
/usr/local/maple15/lib/Calculator.mla

I also obtained an error when asking ln(2)

> ln(2);
Error, (in iroot) powering may produce overflow

[acer]

http://www.mapleprimes.com/questions/130220-Maple-15-X86-64-LINUX-Fedora-16-Log2#comment130515

See also,

https://groups.google.com/forum/#!searchin/comp.soft-sys.math.maple/iroot/comp.soft-sys.math.maple/oSwlrbU2AWI/hHRqO676SYQJ

https://groups.google.com/forum/#!searchin/comp.soft-sys.math.maple/iroot/comp.soft-sys.math.maple/8Hx5jwHMTpI/B0LfnQYsyukJ

[guillaum...@gmail.com]

Ah, thanks. Since I use Maple sparsely, I will simply wait for my department to renew the license and hopefully these problems will vanish.

Still, having Maple answering something false was quite scary ! A good story to tell to calculator-addicted students.