\frametitle{The Substitution Rule for Indefinite Integrals}

  \begin{block}{Substitution Rule}
    If $u = g(x)$ is differentiable function whose range is an interval $I$
    and $f$ is continuous on $I$, then
      \int f(g(x)) \alert<2->{g'(x) \,dx} \;=\; \int f(u) \,\alert<2->{du}
  To remember this rule: note that if $u = g(x)$, then
    \alert{du = g'(x) dx}
  (here we think of $dx$ and $du$ as differentials)
  In other words:
    dx = \frac{du}{g'(x)}
  \alert{If we change the variable from $x$ to $u = g(x)$ we divide by $g'(x)$!}