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\leftline{MATH 132, section 1 -- Calculus for Physical and Life Sciences}
\leftline{Integration By Substitution Practice}
\leftline{January 30, 2008}
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\noindent
Each of the following integrals can be done by the method of $u$-substitution:
\begin{enumerate}
\item Determine the appropriate function $u$, 
\item Compute $du$, 
\item Change the integral to an equivalent form in the new variable $u$, 
\item Integrate, then 
\item Resubstitute $u$ to express the answer in terms of the original variable.
\end{enumerate}
\bigskip
\begin{itemize}
\item $\displaystyle \int x\sqrt{4 - x^2}\ dx$
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\item $\displaystyle \int \cos\theta e^{1 + \sin\theta}\ d\theta$
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\item $\displaystyle \int \cos^3(4\theta) \sin(4\theta)\ d\theta$
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\item $\displaystyle \int \frac{1}{\sqrt{1 - 4x^2}\ dx$
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\item $\displaystyle \int \frac{x}{\sqrt{1 - 4x^2}\ dx$
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\item $\displaystyle \int \frac{1}{x\ln(x)}\ dx$
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\item $\displaystyle \int \frac{\cos(\sqrt{y})}{\sqrt{y}}\ dy$.
\end{itemize}
\end{document}
