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 o
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
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
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
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