\begin{frame}
  \frametitle{The Substitution Rule for Definite Integrals}

  \subruled
  
  \begin{exampleblock}{}
    \vspace{-1ex}
    \begin{talign}
      \int_1^2 \frac{1}{(3-5x)^2}\,dx 
    \end{talign}
    \pause
    We choose $u = \pause 3-5x$. \pause Then $u' = \pause -5$\pause, and hence
    \begin{talign}
      \int_1^2 \frac{1}{(3-5x)^2}\,dx 
      \mpause[1]{&= \int_{u(1)}^{u(2)} \frac{1}{u^2}\, \frac{du}{-5} }
      \mpause{= -\frac{1}{5} \int_{-2}^{-7} \frac{1}{u^2}\, du }\\
      \mpause{&= -\frac{1}{5} \left(-\frac{1}{u}\right) \Big]_{-2}^{-7}}
      \mpause{=  -\frac{1}{5} \left(-\frac{1}{-7} - \left(-\frac{1}{-2}\right)\right)}\\
      \mpause{&= -\frac{1}{5} (\frac{1}{7} - \frac{1}{2})}
      \mpause{=  -\frac{1}{5} \left(\frac{2}{14} - \frac{7}{14}\right)}
      \mpause{=  \frac{1}{14} }
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}