_ -1 / 3 ^ 1 / 3 ^ -1 ( 2 x 1+x^ 2 )+ ^ -1 ( 2 x 1-x^ 2 ) e^ x +1 d x=
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
\[\int_{-1 / \sqrt{3}}^{1 / \sqrt{3}} \frac{\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)}{e^{x}+1} d x=\]
- \(\frac{\pi}{2}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{4 \sqrt{3}}\)
- \(\frac{\pi}{2 \sqrt{3}}\)
Answer
(D) 2 3
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