Diluting The Integrand

Calculus Level 4

0πxsin2xsin(π2cosx)2xπdx\large \displaystyle \int_0^\pi \dfrac{x\sin 2x \sin\left(\frac \pi 2 \cos x\right)}{2x-\pi} \, dx

The above integral can be expressed as ABπC\dfrac{A}{B\pi^C} where AA, BB and CC are positive integers with AA, BB coprime. Find A+B+CA+B+C

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