Ok, thanks a lot. I already reported the bug. El domingo, 30 de octubre de 2022 a las 10:27:23 UTC+1, Frédéric Chapoton escribió:
> 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 >>>>>> >>>>> -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/b27c7ef0-4f84-44aa-be56-ed8ed8e0bfaen%40googlegroups.com.
