Calculus 3 (Math 221) Notes and Study Guide

\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{B.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{B.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{B.2.3} \end{align}