A General Result

Calculus Level 5

$\displaystyle\int_0^{\infty} \dfrac{x^6}{e^{7x}-1} \ dx$

If the above integral has a closed form of $$\dfrac{\Gamma{(a) } \zeta{(b) }} {a^c}$$, find $$2a+b+c$$.

Details and Assumptions:

• $$a, b, c,$$ are all positive integers and they may or may not be different.
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