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∫0πxsin2xsin(π2cosx)2x−π dx\large \displaystyle \int_0^\pi \dfrac{x\sin 2x \sin\left(\frac \pi 2 \cos x\right)}{2x-\pi} \, dx∫0π2x−πxsin2xsin(2πcosx)dx
The above integral can be expressed as ABπC\dfrac{A}{B\pi^C}BπCA where AAA, BBB and CCC are positive integers with AAA, BBB coprime. Find A+B+CA+B+CA+B+C
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