\begin{frame} \frametitle{The Substitution Rule: Exercises} \begin{exampleblock}{} Evaluate \begin{talign} \int x^2 e^{x^3}\, dx \end{talign} \pause We take $u = \pause x^3$\pause, then $u' = \pause 3x^2$ \pause and \begin{talign} \int x^2 e^{x^3}\, dx \mpause[1]{ &= \int x^2 e^{u} \, \frac{du}{3x^2} } \\ \mpause{ &= \frac{1}{3} \int e^u \, du } \\ \mpause{ &= \frac{1}{3}e^u + C }\\ \mpause{ &= \frac{1}{3}e^{x^3} + C } \end{talign} \pause\pause\pause \end{exampleblock} \end{frame}