^ -1 x (1-x^ 2 )^ 3 / 2 d x is equal to
Mathematics · JEE Main · NTA Exams — Integral Calculus
\[\int \frac{\sin ^{-1} x}{\left(1-x^{2}\right)^{3 / 2}} d x \text { is equal to }\]
- \(\frac{x}{\sqrt{1-x^{2}}} \sin ^{-1} x+\frac{1}{2} \log \left|\sqrt{1-x^{2}}\right|+c\)
- \(\frac{x}{\sqrt{1-x^{2}}} \sin ^{-1} x+\frac{1}{2} \log \left|1-x^{2}\right|+c\)
- \(\frac{x}{\sqrt{1-x^{2}}} \sin ^{-1} x+\frac{1}{4} \log \left|\sqrt{1-x^{2}}\right|+c\)
- none of these
Answer
(B) x 1-x^ 2 ^ -1 x+ 1 2 |1-x^ 2 |+c
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