Incorrect integral in Maxima

[kcrisman]

See this ask.sagemath.org question.

sage: integral(log(cot(x)-1),x,0,pi/4)

ValueError: Integral is divergent.

But according to the poster it is pi log(2) / 8. And indeed in the most recent Maxima (5.28) we have

(%i5) display2d:false;

(%o5) false
(%i6) integrate(log(cot(x)-1),x,0,%pi/4);

Is %pi/8 an ?integer?

n;
Is %pi/4 an ?integer?

n;
Is 2*%pi an ?integer?

n;
(%o6) -(%i*(2*li[2](%i+1)-2*li[2](1-%i))+%pi*log(2))/4
 +%i*li[2]((%i+1)/2)/2-%i*li[2](-(%i-1)/2)/2

though with the interaction this is not an improvement we can immediately use.

Component: calculus

Author: Peter Bruin

Branch: 59bb147

Reviewer: Ralf Stephan, Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/13733

[kcrisman]

comment:1

According to the upstream report, that problem is also fixed here and there is also a commit of the integral in question as a test.

expand(integrate(log(cot(x)-1),x,0,%pi/4));
-%i*li[2](%i+1)/2+%i*li[2](%i/2+1/2)/2-%i*li[2](1/2-%i/2)/2+%i*li[2](1-%i)/2-%pi*log(2)/4$

So I guess when the next Maxima after 5.29.1 is ready and we put it in, we can try to close this report with a doctest.

[kcrisman]

Upstream: Fixed upstream, but not in a stable release.

[kcrisman]

comment:2

See #13973 for where we might fix this.

[pjbruin]

comment:6

Maxima 5.33 returns the answer without asking any questions.