Pretty Nice Integral
Calculus
Level
5
\[ \displaystyle \int_{0}^{\infty} \dfrac{x^{5}\mathrm{d}x}{e^{5x} -1} = \dfrac{1}{a^{b}}\zeta(c)\Gamma(c)\\ \]
With \(a,b,c\) are positive integers with prime number \(a\), find \(\dfrac{5}{6}abc^2\)
\(\text{ Details and Assumptions }\)
1.)\(\zeta(x) \) is the Riemann Zeta Function
2.)\(\Gamma(x)\) is the Gamma Function
by
Upanshu Gupta