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

If I type

integrate(x^3/(exp(x)-1),x,0,infinity) I get -1/15

pi^4 + limit(-1/4x^4 + x^3log(-e^x + 1) + 3x^2dilog(e^x) - 6xpolylog(3, e^x) + 6polylog(4, e^x), x, +Infinity, minus)

The command numerical_integral(x^3/(exp(x)-1),0,infinity) gives 6.4939394075

I have two questions :

- How do I evaluate the limit ?
- The correct answer is pi^4/15(=6.49393940226683) : why SageMath does not give it with symbolic integration ?

Thanks

This seems closely related to https://groups.google.com/forum/#!top...