Paneer Definite Masala 3

Calculus Level 5

0cosxt1+t2dt \large \int_0^\infty \dfrac{ \cos xt}{1+t^2} \, dt

If the integral above is equal to ab \dfrac ab, where aa and bb are coprime positive integers, find a+b+aba+b+ab.

Take x=ln3π5x=\ln \frac{3\pi}5

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