A calculus problem by Kishore S Shenoy

Calculus Level 3

\[\large\int_0^\pi \dfrac{x\sin x}{1+\cos^2x}\, dx\]

If the above integral can be written as \(\dfrac {A\pi^B}C\), where \(A\), \(B\) and \(C\) are positive integers with \(A\) and \(C\) being coprime integers. Find \(A+B+C\).

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