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\title{Math 1b. Integration by Parts}

\date{Spring 2006}

\begin{document}

\maketitle




Evaluate each of the following integrals
\begin{enumerate}

\item 
$\displaystyle \int x \cos 2x \, dx$

\vfill



\item 
$\displaystyle \int \frac{\ln x}{x^2} \, dx$

\vfill

\item 
$\displaystyle \int_{-1}^{1/\sqrt{2}}  x^2 \arctan x \, dx$.

\vfill

\clearpage

\item 
$\displaystyle \int x^2 \sin x \, dx$

\vfill

\item 
$\displaystyle \int e^x \sin x \, dx$

\vfill

\item 
$\displaystyle \int x e^x \sin x \, dx$

\vfill

\item 
$\displaystyle \int_1^{e} x^2 \ln x \, dx$

\vfill

\end{enumerate}



 \end{document}