Integrating Difference Of Arctangents?

Calculus Level 3

0tan1(πx)tan1(x)xdx=AπBlnπC \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,CA,B,C with A,CA,C coprime. Find A×B×CA\times B\times C.

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