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

×

Problem Loading...

Note Loading...

Set Loading...