# Yet another Integral

Calculus Level 5

$\int_0^\infty \dfrac{\sin(2\cos^2(x)) \cosh(\sin(2x))}{1+x^2} dx=\dfrac{a\pi}{b}\sin\bigg(c+\dfrac{1}{e^d}\bigg)$ If the above equation is true for integers $$a,b,c,d,$$ with $$\text{gcd}(a,b) =1$$, find $$(a+b+c)^d$$.

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