Do you know the best way to integrate this?

Calculus Level 4

\[\large \int_{0}^{1} x^2 \tan^{-1} x \,dx = \dfrac{\pi}{A} -\dfrac{B-\ln C}{D}\] If the above equation holds true for positive integers \(A\), \(B\), \(C\) and \(D\) such that \(D\) is minimized, find \(A+B+C+D\).

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