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∫0∞cosxt1+t2 dt \large \int_0^\infty \dfrac{ \cos xt}{1+t^2} \, dt ∫0∞1+t2cosxtdt
If the integral above is equal to ab \dfrac abba, where aaa and bbb are coprime positive integers, find a+b+aba+b+aba+b+ab.
Take x=ln3π5x=\ln \frac{3\pi}5x=ln53π
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