Hyperbolic Integral

Calculus Level 5

\[ \large \int_0^\infty \dfrac{ \ln x}{\cosh^2 x} \, dx =\ln{ \left( \frac { A\pi }{ B } \right) } -C\gamma \]

The equation above holds true for positive integers \(A, B\) and \(C\), with \(A,B\) coprime. Find \(A+B+C\).

Notation: \( \gamma\) denote the Euler-Mascheroni constant.

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