Ugly result for exponential integral

[orlitzky]

As reported in this sage-support thread:

http://groups.google.com/group/sage-support/browse_thread/thread/793c2bdb3db1f02c

We expect,

sage: integral( x / (exp(x) - 1) , (x,0,oo))
pi^2/6

but get,

sage: integral( x / (exp(x) - 1) , (x,0,oo))
-1/6*pi^2 + limit(-1/2*x^2 + x*log(-e^x + 1) + polylog(2, e^x), x, +Infinity)

The above might not be incorrect, but it is not very useful either.

CC: @kcrisman

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/12145

[orlitzky]

comment:2

Same result from Maxima 5.27:

(%i1) display2d: false;

(%o1) false
(%i2) f: x/(%e^x - 1);

(%o2) x/(%e^x-1)
(%i3) integrate(f, x, 0, inf);

(%o3) 'limit(li[2](%e^x)+x*log(1-%e^x)-x^2/2,x,inf,minus)-%pi^2/6

[c22b6800-ec0b-4cbf-94c4-0a74aecc2093]

comment:7

more tests:

sage: giac('integrate(x / (exp(x) - 1), x, 0, inf)')
pi^2/6
sage: integrate(x / (exp(x) - 1), x, 0, oo, algorithm='sympy')
integrate(x/(e^x - 1), x, 0, +Infinity)

i think this is another reason to make more user friendly the functionality that is offered through giac; stay tuned at the giac interface wiki.