Question

Evaluate

$\int x^{}{sin}^{-1}x$ $dx$.

Answer 1

$\begin{array}{c}{\int }^{}x{\sin }^{-1}xdx\\ =\frac{x^2{\sin }^{-1}x}{2}-{\int }^{}\frac{x^2}{2\sqrt{1-x^2}}dx\\ =\frac{x^{2}si{n}^{-1}\left(x\right)}{2}-\frac{si{n}^{-1}\left(x\right)}{4}+\frac{x\sqrt{1-x^2}}{4}+C\end{array}$