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

  \subrule 
  
  \begin{exampleblock}{}
    \begin{talign}
      \int 2x\sqrt{1 + x^2} dx 
    \end{talign}
    \pause
    We choose $u = \pause 1 + x^2$. \pause Then $u' = \pause 2x$\pause, and hence
    \begin{talign}
      \int 2x\sqrt{1 + x^2} dx 
      \mpause[1]{&= \int 2x\sqrt{u}\, \frac{du}{2x} }
      \mpause{= \int \sqrt{u}\, du}\\
      \mpause{&= \frac{2}{3}u^{\frac{3}{2}} + C}
      \mpause{= \frac{2}{3}(1+x^2)^{\frac{3}{2}} + C}
    \end{talign}
  \end{exampleblock} 
  \vspace{10cm}
\end{frame}