\[\int_{0}^{\infty} \dfrac{\arctan{(x)}\log{(1+x^2)}}{1+x^2}\mathrm{d}x=\dfrac{\pi^2}{A} \log {2}+\dfrac{B}{C} \zeta (3)\] \(A, \ B\) and \(C\) are integers. \(B\) and \(C\) co-prime. Find \(A+B+C\)

This problem is the result of my carelessness :) Here's the original problem.

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