# Integrating Difference Of Arctangents?

Calculus Level 3

$\large \int_{0}^{\infty} \dfrac{\tan^{-1}(\pi x) - \tan^{-1}(x)}{x}\, dx = A\pi^{B}\dfrac{\ln \pi}{C}$

The equation holds true for positive integers $$A,B,C$$ with $$A,C$$ coprime. Find $$A\times B\times C$$.

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