integrate x^3/(exp(x)-1) between 0 and infinity

savecancel

For this type of computation, it is worth trying with some algorithm different from the default one (Maxima):

sage: integrate(x^3/(exp(x)-1),x,0,infinity, algorithm='giac')
1/15*pi^4

EDIT: the above works only for Sage 8.0.beta5 and higher versions (after the ticket https://trac.sagemath.org/ticket/22891 has been merged). This will therefore be available in the next stable release of Sage (8.0).

To complement Eric's answer, you will can use giac integration algorithm from Sage version 8.0.beta4, so you should either install the latest development version, or wait for the official 8.0 version. Also, it is not enough to install giac package, you should also install the giacpy_sage package.