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Tricky Definite Integral

Calculus Level 5

\[ \large \int _0^{\sqrt{3}}\frac{1}{1+x^2}\sin ^{-1}\left(\frac{2x}{1+x^2}\right) \, dx = \, ? \]

\[\frac{\pi ^2}{4}\] \[\frac{\pi ^2}{9}\] \[\frac{3\pi ^2}{36}\] \[\frac{7\pi ^2}{72}\]

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by Benny Joseph

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