# Integrate the Functional

Calculus Level 2

A function $$f(x)$$ satisfies the functional equation $f(\tan \theta)=\frac{\sin^2 2\theta}{4}$ for all real $$\theta$$. If $$\displaystyle \int_{0}^{\infty}f(x) \ dx$$ is equal to $$\dfrac{\pi^a}{b}$$ for positive integers $$a,b$$, then what is the value of $$a+b$$?

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