Thursday, 28 March 2019

calculus - The integral $intlimits_0^inftyfrac{x^4e^x}{(e^x-1)^2} mathrm{d}x$

How to calculate the following integral $$\int_0^\infty\frac{x^4e^x}{(e^x-1)^2}\mathrm{d}x$$
I would like to solve this integral by means of two different ways: for example, integration by parts and using Residue Theorem.

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