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

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

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