Paneer Definite Masala 3

Calculus Level 5

\[ \large \int_0^\infty \dfrac{ \cos xt}{1+t^2} \, dt \]

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

Take \(x=\ln \frac{3\pi}5\)

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