# Diluting The Integrand

Calculus Level 4

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

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

×