Questions

$\int \frac{x \sin^{- 1} x}{\sqrt{1 - x^{2}}} d x =$

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−x−1−x2sin−1x+c

x2−1−x2sin−1x+c

x+1−x2sin−1x+c

x−1−x2sin−1x+c

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detailed solution

Correct option is D

f(x)=sin−1⁡x⋅g(x)=x1−x2 By using integration by parts ∫xsin−1x1−x2dx= sin-1x-1-x2 -∫11−x2-11−x2 dx =x−1−x2sin−1x+c

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