Question

Which substitution can also be used before integrating by parts for \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx?\]

Options

• \[\sin^{-1}x=\theta\]

• \[x^2=\theta\]

• \[\cos^{-1}x=\theta\]

• \[\sqrt{1-x^2}=\theta\]

Answer 1

An alternative begins with \(\sin^{-1}x=\theta\). After this substitution, the resulting integral can be evaluated by integration by parts.