Section C.2 Integrals Involving Inverse Trigonometric Functions
\begin{align}
\int u^n \sin^{-1} u\ du \amp=\amp \frac{1}{n+1} \left[ u^{n+1} \sin^{-1} u - \int \frac{u^{n+1} du}{\sqrt{1-u^2}} \right], \; n \neq -1\tag{C.2.1}\\
\int u^n \cos^{-1} u\ du \amp=\amp \frac{1}{n+1} \left[ u^{n+1} \cos^{-1} u + \int \frac{u^{n+1} du}{\sqrt{1-u^2}} \right], \; n \neq -1\tag{C.2.2}\\
\int u^n \tan^{-1} u\ du \amp=\amp \frac{1}{n+1} \left[ u^{n+1} \tan^{-1} u + \int \frac{u^{n+1} du}{1+u^2} \right], \; n \neq -1\tag{C.2.3}
\end{align}