# Inspired by Jake Lai

Calculus Level 5

$\int _{ 0 }^{ \pi/2 }{ (\sin x) \ln { \left( \cos {x} \right) } \ln { \left( \sin {x} \right) } \, dx } =A-\frac{B\pi ^C}{D}-\ln {E}$

Where $$A,B,C,D, E$$ are positive integers, $$E$$ is not a perfect power, and $$\gcd{(B,D)}=1$$.

Find the value of $$A+B+C+D+E$$

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