Hot Integral - 14

Calculus Level 5

\[\displaystyle \int\limits_{0}^{\infty} f^2(x) dx = \frac{\pi^A}{B}\left(\log(C) - \psi(\frac{D}{E})\right)\]

where \[f(x) = \int\limits_{0}^{\infty} \cos(x\cosh(t)) dt\]

Calculate \(A+B+C+D+E\)

Clarifications:

  • \(\psi(n)\) is polygamma function.
  • \(A,B,C,D,E\) are integers.
  • \(gcd(D,E)=1\)

This is a part of Hot Integrals

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