\begin{frame} \frametitle{The Substitution Rule: Exercises} \begin{exampleblock}{} \begin{malign} \int (x+1)\sqrt{2x+x^2}\, dx &&\text{take $u = \mpause[1]{2x+x^2}$\mpause{, then $u' = 2(1+x)$}} \end{malign} \pause\pause \end{exampleblock} \pause \begin{exampleblock}{} \begin{malign} \int (3t + 2)^{2.4}\, dx &&\text{take $u = \mpause[1]{3t+2}$} \end{malign} \pause \end{exampleblock} \pause \begin{exampleblock}{} \begin{malign} \int e^x\cos e^x\, dx &&\text{take $u = \mpause[1]{e^x}$} \end{malign} \pause \end{exampleblock} \pause \begin{exampleblock}{} \begin{malign} \int \frac{\sin \sqrt{x}}{\sqrt{x}}\, dt &&\text{take $u = \mpause[1]{\sqrt{x}}$\mpause{, then $u' = \frac{1}{2\sqrt{x}}$}} \end{malign} \pause\pause \end{exampleblock} \pause \begin{exampleblock}{} \begin{malign} \int \frac{(\ln x)^2}{x} \, dt &&\text{take $u = \mpause[1]{\ln x}$} \end{malign} \pause \end{exampleblock} \pause \begin{exampleblock}{} \begin{malign} \int (x^3+3x)(x^2+1)\, dt &&\text{take $u = \mpause[1]{x^3+3x}$\mpause{, then $u' = 3(x^2+1)$}} \end{malign} \pause\pause \end{exampleblock} \end{frame}