\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Some antiderivatives can be computed
using ``rationalizing substitutions'' to change the integrals into
integrals of rational functions which then can be computed using
partial fractions. Here are some examples.

\medskip

\noindent a) $\int {1 \over { x+3\sqrt x+2}} \, dx$ \quad
{(Try $t = \sqrt{x}$.)}

\medskip

\noindent b) $\int {{e^{x} + 1} \over { e^{2x} + 1}} \, dx$ \quad {(Try $t =
e^x$.)}

\medskip

\noindent c) $\int {{\cos \theta} \over {1-(\sin \theta)^2}}\,
d\theta$\quad {(Try $t = \sin \theta^*$\vfootnote*{You've
just integrated sec. Was the result ln(sec + tan)?}.)}


\vfil\eject\end

