# A Cool Integral in Disguise

Calculus Level 5

$\large \displaystyle \int_0^\infty \dfrac{x^7 (e^{3x} - e^x)}{(e^x -1)^4} \, dx = \dfrac{n! \pi^n}{m}$

If the above integral is true for positive integers $$n$$ and $$m$$, what is the value of $$n + m$$?

You may want to look up the value of $$\zeta(2n)$$ for a certain positive integer $$n$$.

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