# Paneer Definite Masala 4

Calculus Level 5

$\large\int_{-\pi /4}^{\pi /4} \dfrac{2\pi - \sin (2\pi x) }{2 - \cos2x } \, dx$

If the integral above is equal to $$\dfrac{A\pi^B}{C\sqrt D} + E$$, where $$A,B,C,D$$ and $$E$$ are non-negative integers with $$A,C$$ coprime and $$D$$ square-free, find $$A+B+C+D+E$$.

×