Is there an indefinite integral for this?

Calculus Level 4

0x4ex(ex1)2dx\large \displaystyle\int_0^{\infty}\frac{x^4e^x}{(e^x-1)^2} \, dx

The integral above equals to abπ4 \frac ab \pi^4 for coprime positive integers a,ba,b and that you're given j=11j4=π490 \displaystyle \sum_{j=1}^\infty \frac1{j^4} = \frac{\pi^4}{90} .

Find a+ba+b

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