# Is there an indefinite integral for this?

Calculus Level 4

$\large \displaystyle\int_0^{\infty}\frac{x^4e^x}{(e^x-1)^2} \, dx$

The integral above equals to $$\frac ab \pi^4$$ for coprime positive integers $$a,b$$ and that you're given $$\displaystyle \sum_{j=1}^\infty \frac1{j^4} = \frac{\pi^4}{90}$$.

Find $$a+b$$

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