The factor-2 problem is also present for the integral with no bounds.
Please report in maxima's bug reporting site.
(%i20) integrate(x*log(x)^4/(x^2 + 1),x);
4 2
2 log (x) log(x + 1) 2 2
(%o20) - (3 ((- ---------------------) + li (- x ) - 2 log(x) li (- x )
3 5 4
3 2
4 log (x) li (- x )
2 2 2
+ 2 log (x) li (- x ) -
-------------------))/2
3 3
(%i21) diff(%,x);
4
2 x log (x)
(%o21) -----------
2
x + 1
Le mardi 25 octobre 2022 à 00:17:07 UTC+2, pvit...@gmail.com a écrit :
> Thank you very much for the analysis. If I understand correctly, the bug
> is in this part of the integral: x*log(x)^4/(x^2 + 1)
>
> I will try to report the bug to maxima. But, as far I can see
> https://sourceforge.net/p/maxima/bugs/ is very quiet, with few answers to
> the reports.
>
> El lunes, 24 de octubre de 2022 a las 21:33:41 UTC+2, Frédéric Chapoton
> escribió:
>
>> where we can see that there is a factor 2 between the wrong symbolic
>> value and the correct numeric value
>>
>> This should be filed as a bug in maxima.
>>
>> Le lundi 24 octobre 2022 à 21:24:30 UTC+2, Frédéric Chapoton a écrit :
>>
>>> and one more step :
>>>
>>> sage: integrate(x*log(x)^4/(x^2 + 1), x,0,1).n()
>>> 1.45817965567036
>>> sage: (x*log(x)^4/(x^2 + 1)).nintegral(x,0,1)
>>> (0.7290898278351722, 2.48288156701193e-09, 357, 0)
>>> sage: integrate(-log(x)^4/(x^2 + 1), x,0,1).n()
>>> -23.9077878738501
>>> sage: (-log(x)^4/(x^2 + 1)).nintegral(x,0,1)
>>> (-23.90778787384685, 1.267767046897461e-08, 483, 0)
>>>
>>>
>>> Le lundi 24 octobre 2022 à 21:19:46 UTC+2, Frédéric Chapoton a écrit :
>>>
>>>> more study of the bug (coming from maxima)
>>>>
>>>> sage: C=x^2*(log(x))^4/((x+1)*(1+x^2))
>>>> sage: aa,bb=C.partial_fraction_decomposition()
>>>> sage: integral(aa,x,0,1)
>>>> -5/128*pi^5 + 45/64*zeta(5)
>>>> sage: integral(bb,x,0,1)
>>>> 45/4*zeta(5)
>>>> sage: _+__
>>>> -5/128*pi^5 + 765/64*zeta(5)
>>>> sage: _.n()
>>>> 0.440633136273039
>>>> sage: aa.nintegral(x,0,1)
>>>> (-11.58934902297507, 5.068708119893017e-08, 525, 0)
>>>> sage: bb.nintegral(x,0,1)
>>>> (11.66543724536065, 4.943314557692702e-08, 525, 0)
>>>> sage: integral(aa,x,0,1).n()
>>>> -11.2248041090899
>>>> sage: integral(bb,x,0,1).n()
>>>> 11.6654372453629
>>>>
>>>>
>>>>
>>>> Le lundi 24 octobre 2022 à 00:14:09 UTC+2, pvit...@gmail.com a écrit :
>>>>
>>>>> I am using Sage 9.7 running in Arch linux over WSL2
>>>>>
>>>>> I get different results for an integral using numerical integration
>>>>> (which seems to agree with Mathematica) and symbolic integration:
>>>>>
>>>>> numerical_integral(x^2*(log(x))^4/((x+1)*(1+x^2)),0,1)
>>>>> (0.07608822217400527, 1.981757967172001e-07)
>>>>>
>>>>> integral(x^2*(log(x))^4/((x+1)*(1+x^2)),x,0,1)
>>>>> 6*I*polylog(5, I) - 6*I*polylog(5, -I) + 765/64*zeta(5)
>>>>> integral(x^2*(log(x))^4/((x+1)*(1+x^2)),x,0,1).n()
>>>>> 0.440633136273036
>>>>>
>>>>
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