JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}} d x=

View answer and explanation

Correct option: A

\frac{x}{\sqrt{1-x^2}} \sin ^{-1} x+\frac{1}{2} \log \left(1-x^2\right)+c

Option A (

\frac{x}{\sqrt{1-x^2}} \sin ^{-1} x+\frac{1}{2} \log \left(1-x^2\right)+c

) is correct because substituting

\sin t = x

simplifies the integral, and integration by parts yields the correct result.

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