Pretty Nice Integral

Calculus Level 5

0x5dxe5x1=1abζ(c)Γ(c) \displaystyle \int_{0}^{\infty} \dfrac{x^{5}\mathrm{d}x}{e^{5x} -1} = \dfrac{1}{a^{b}}\zeta(c)\Gamma(c)\\

With a,b,ca,b,c are positive integers with prime number aa, find 56abc2\dfrac{5}{6}abc^2

 Details and Assumptions \text{ Details and Assumptions }
1.)ζ(x)\zeta(x) is the Riemann Zeta Function
2.)Γ(x)\Gamma(x) is the Gamma Function

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