# Integrating mixture of functions

Calculus Level 4

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

The equation above holds true for some positive integers $A$ and $B$. Find $A+B$.

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