# 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 $$A+B$$.

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