499 Followers Problem

Calculus Level 4

∫−1/31/3cos⁡−1(2x1+x2)+tan⁡−1(2x1−x2)ex+1 dx\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

πAB, \dfrac{ \pi}{A\sqrt B} ,

where AA and BB are positive integers with BB square-free, find A+BA+B.

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