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\title{Math 1b. Partial Fractions}

\date{Spring 2006}

\begin{document}

\maketitle




Evaluate each of the following integrals
\begin{enumerate}

\item 
$\displaystyle \int \frac{5x + 7}{(x+1)(x + 2)} \, dx$

\vfill



\item 
$\displaystyle \int \frac{x^2 + 3x -1}{x(x + 1)(x -2)} \, dx$

\vfill


\item 
$\displaystyle \int \frac{x^2  -1}{x(x^2 + 4)} \, dx$

\vfill

\clearpage

\item 
$\displaystyle \int \frac{3x^2 + 7x + 5}{(x + 1)(x^2 + 2x + 2)} \, dx$

\vfill

\item 
$\displaystyle \int \frac{4x^2  - 3x + 2}{x(2x -1)^2} \, dx$

{\em Hint}: Let
$\displaystyle \frac{4x^2  - 3x + 2}{x(2x -1)^2} = \frac{A}{x} + \frac{B}{2x -1} + \frac{C}{(2x - 1)^2}$.

\vfill

\item 
$\displaystyle \int \frac{1}{x^2 + 2x + 2} \, dx =  \int \frac{1}{(x^2 + 2x + 1) + 1} \, dx$

\vfill


\end{enumerate}



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