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Question
Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]
Options
\[x+\sqrt{1-x^2}\sin^{-1}x+C\]
\[-x-\sqrt{1-x^2}\sin^{-1}x+C\]
\[x-\sqrt{1-x^2}\sin^{-1}x+C\]
\[\sqrt{1-x^2}\sin^{-1}x-x+C\]
MCQ
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Solution
Use \(u=\sin^{-1}x\) and \(v=-\sqrt{1-x^2}\). Then \(\int u\,dv=-\sqrt{1-x^2}\sin^{-1}x+x+C\), which is the stated result.
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