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/06fc8cdf-6742-424c-b2c2-7559aaf08934n%40googlegroups.com.
