Do you know the best way to integrate this?

Calculus Level 4

01x2tan1xdx=πABlnCD\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 AA, BB, CC and DD such that DD is minimized, find A+B+C+DA+B+C+D.

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