Integral representation of Riemann Zeta Function

[foin137]

Sympy 1.12 cannot currently solve the definite integral

$$\int_0^\infty \frac{x^{s-1}}{e^x-1}dx=\Gamma(s)\zeta(s)$$

which is a representation of the Riemann Zeta function (https://en.wikipedia.org/wiki/Riemann_zeta_function)

Instead, for example the code

import sympy
sympy.init_printing(use_unicode=False, wrap_line=False)
x = sympy.Symbol('x')
sympy.integrate(x**2 * 1/(sympy.exp(x)-1),(x,0,sympy.oo))

returns the unevaluated integral.

I tried to look into the documentation and code where one might add this to sympy, but I wasn't able to find an easy fix that was doable by me (also I am no expert in integration algorithms).

This issues was also raised in #24431 and #8169 and #23326

Maybe it can be solved by adding the integral representations of the Zeta functions?