> > *numerical way* > (double checked by Wolfram Alpha > <http://www.wolframalpha.com/input/?i=int%20from%202%20to%203%20of%201%2Flog%28x%29%5E2> > > and Maple): > > sage: numerical_integral(1/log(x)^2,2,3) > > (*1.273097216447114*, 1.4134218422857824e-14) > > *symbolic way* > (I think this is wrong) >
Of course you are right: sage: (plot(1/(ln(x))^2, x,2,3)+plot(1,x,2,3,color='red')).show(ymin=0) > > sage: N(integral(1/log(x)^2,(x,2,3))) > *0.536566859259958* > > > > This is probably a problem with our evaluation of incomplete gamma functions, or possibly of Maxima giving a bad branch or something? sage: integral(1/(ln(x))^2, x,2,3) gamma(-1, -log(3)) - gamma(-1, -log(2)) sage: integral(1/(ln(x))^2, x) gamma(-1, -log(x)) Maxima: (%i3) integrate(1/log(x)^2,x); (%o3) gamma_incomplete(- 1, - log(x)) This is ugly: sage: plot(lambda t: numerical_integral(1/ln(x)^2,2,t)[0],2,3)+plot(lambda t: gamma(-1, -log(t)).real(),2,3,color='red') I'm not at all an expert on such special functions, but this should be enough for someone else to diagnose it pretty quickly. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
