I have been attempting to solve the following integral as part of a solid state physics problem:
$$\int_{0}^{2}\frac{x^2e^x}{(e^x-1)^2}\,dx$$
Can someone please explain how this can be evaluated?
2026-04-08 07:10:41.1775632241
Evaluating improper definite integrals
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According to Maple the answer is $$-2\,{\it dilog} \left( {{\rm e}^{2}} \right) -4\,{\frac {{{\rm e}^{2}} }{{{\rm e}^{2}}-1}}.$$ AFAIK this can't be simplified to anything more elementary. Numerically the value is approximately $1.801718567$.