Cos cosine has it's own problems..

Calculus Level 5

$\large \int_{0}^{\frac{\pi}{2}} \cos^{-1}\left(\frac{\cos{x}}{1+2\cos{x}}\right) dx = \frac{A}{B} \pi^2$

Positive coprime integers $A$ and $B$ satisfy the equation above. If $A\times B=N!$ , find $N$ .

1 solution

Mark Hennings
Sep 17, 2017

This is the classic Coxeter integral. Its evaluation as $\tfrac{5}{24}\pi^2$ is lengthy, but one approach can be found here