# It isn't what it looks!

Calculus Level 5

$\displaystyle \int_0^{2\pi} x^2\left( \ln \left| 2 \sin\dfrac{x}{2} \right| \right)^{2} \, dx= \dfrac{A\pi^C}{B}$

If the equation above holds true for integers $$A,B$$ and $$C$$ with $$A,B$$ coprime positive integers, find $$A+B+C$$.

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