Seven seas in this world!

Calculus Level 4

0x71exdx \large \int_0^\infty \dfrac{x^7}{1-e^x} \, dx

If the integral above is equal to ABπC -\frac AB \pi^C, where A,BA,B and CC are coprime positive integers with A,BA,B coprime, find A+B+CA+B+C.

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