# The 2 seems out of place

Calculus Level 4

$\displaystyle\int_0^{\frac{\pi}{2}}x\ln(\sin 2x)\text{ }dx$

The integral above is equal to $$\dfrac{-\pi^A\ln B}{C},$$ where $$A$$, $$B$$, and $$C$$ are positive integers and $$B$$ is minimized. Find $$A+B+C.$$

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