# Dogbone

Calculus Level 5

$\large\int_0^1 \frac{\sqrt{1-x^2}}{x^8+1}\,dx \; = \; \tfrac{\pi^A}{\sqrt{B}}\left [ \sqrt{\cos\left(\tfrac{\pi}{C}\right)} \cos\left(\tfrac{D\pi}{E}\right) - \sqrt{\sin\left(\tfrac{\pi}{C}\right)} \sin\left(\tfrac{F\pi}{E}\right)\right ]$

Given that the equation above holds true, where $$A,B,C,D,E$$ and $$F$$ are positive integers such that $$\tfrac{F\pi}{E} < \tfrac{\pi}{C} < \tfrac{D\pi}{E}$$ are acute angles, and $$D,E,F$$ are pairwise coprime, find the value of $$A+B+C+D+E+F$$.

×