# Now this is easier right?

Calculus Level 5

$\large \displaystyle \int_0^{\frac{\pi}{2}} x\ln^{2}(\sin 2x)\mathbb{d}x = \dfrac{\pi^{A}}{B}\ln^{C}(D) +\dfrac{\pi^{E}}{F}$ If the above integral is true for positive integers:$$A,B,C,D,E,F$$
and $$D$$ is a prime, find:
$A+B+C+D+E+F$

×