Integrating mixture of functions

Calculus Level 5

\[ \large \int^{\infty }_{0}\frac{\cos ( \pi x) }{4x^{2}+1} \, dx=\dfrac1B{\pi e^{\frac{-\pi }{A} }} \]

The equation above holds true for some positive integers \(A\) and \(B\). Find \(A+B\).


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This problem is part of the set of complex analysis problems.
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