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\title{\vspace*{-1.5in}\textbf{Math 2300-007: Integration By Parts}}
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%\underline{Math 1300-400: Quiz 1}
\lhead{Math 2300-007: Calculus II}
\chead{January 19, 2018}
\rhead{Integration By Parts}
\vspace{-.5in}
\noindent
\textbf{Key points:}
\begin{itemize}
\item Integration by parts comes from the \rule{1.5in}{0.5pt} rule for derivatives:\vskip1.5in
\item The integration by parts formula is given by\[\boxed{\phantom{\Bigg| whooooooooooooasdfasdfasdfooo!}}\]
\item Advice for choosing $u$ and $dv$:\vskip1in
\item Use integration by parts when...\vskip1in
\end{itemize}
Compute the following integrals using integration by parts:
\vskip12pt
\begin{enumerate}
 \item $\displaystyle \int x\cos{x}\,dx$ \vfill
 \item $\displaystyle  \int_0^2 xe^x\,dx$ \vfill
\newpage
 \item $\displaystyle \int_4^9 \frac{\ln(y)}{\sqrt{y}}\,dy$\vskip6cm
 \item $\displaystyle \int \theta^2\sin(3\theta)\,d\theta$\vskip6cm
 \item $\displaystyle \int \arctan{x}\,dx$\vskip6cm
 \item $\displaystyle \int \ln{x}\,dx$\vskip6cm
\item $\displaystyle \int \left(\ln{x}\right)^2\,dx$\vskip6cm
\item $\displaystyle \int_0^1\frac{x+1}{e^{x}}\,dx$\vskip6cm
\item $\displaystyle \int e^t\cos{t}\,dt $\vskip6cm
\item $\displaystyle \int \sec^3{x}\,dx$\vskip6cm
\item $\displaystyle \int_1^{\sqrt{3}}\arctan\left(\frac{1}{x}\right)dx$\vskip6cm
\end{enumerate}
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