# Hot Integral - 14

Calculus Level 5

$\int_0^\infty f^2(x)\ dx = \frac{\pi^A}{B}\left(\log(C) - \psi \left(\frac{D}{E}\right)\right)$

where $$\displaystyle f(x) = \int_0^\infty \cos(x\cosh(t))\ dt$$ and $$A$$, $$B$$, $$C$$, $$D$$, and $$E$$ are integers with $$D$$ and $$E$$ being positive coprime integers. Calculate $$A+B+C+D+E$$.

Notations: $$\psi(n)$$ is polygamma function.

This is a part of Hot Integrals

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