_ 0 ^ 1 / 2 e^ x ( ^ -1 x- x (1-x^ 2 )^ 3 / 2 ) d x=
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
\[\int_{0}^{1 / 2} e^{x}\left(\sin ^{-1} x-\frac{x}{\left(1-x^{2}\right)^{3 / 2}}\right) d x=\]
- \(\sqrt{e}\left(\frac{\pi}{6}-\frac{1}{\sqrt{3}}\right)+1\)
- \(\sqrt{e}\left(\frac{\pi}{6}+\frac{2}{\sqrt{3}}\right)+1\)
- \(\sqrt{e}\left(\frac{\pi}{6}-\frac{2}{\sqrt{3}}\right)+1\)
- \(\sqrt{e}\left(\frac{\pi}{6}+\frac{1}{\sqrt{3}}\right)+1\)
Answer
(C) e ( 6 - 2 3 )+1
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