499 Followers Problem
Calculus
Level
4
\[\large \int_{-{1} / {\sqrt{3}}}^{{1} / {\sqrt{3}}}\frac{\cos^{-1}\left ( \frac{2x}{1+x^{2}} \right )+\tan^{-1}\left ( \frac{2x}{1-x^{2}} \right )}{e^{x}+1} \, dx\]
If the integral above can be expressed in the form
\[ \dfrac{ \pi}{A\sqrt B} , \]
where \(A\) and \(B\) are positive integers with \(B\) square-free, find \(A+B\).
by
Chinmay Sangawadekar