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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 4}\quad {\sl Feb. 16, 1995}

\begin{enumerate}
\problemspace
\item 
  \begin{enumerate}[a)]
  \item Give the general form of the partial fraction decomposition of
  $$\frac{x+d}{(x-a)(x^2+b)^2(x+c)^3}\quad (b>0)$$
  (Do not solve for the constants).
  \answerspace

  \problemspace
  \item Integrate $\int\frac{1}{x(x^2+1)(x-1)}\,dx$.
  \answerspace

  \end{enumerate}

\problemspace
\item
  \begin{enumerate}[a)]
  \item Use an appropriate substitution to transform the integral 
  $$\int \frac{1}{\cos^2(\theta) + \cos(\theta) + 1}\,d\theta$$
  into an integral of a rational function. (Do not evaluate the integral.)
  \answerspace

  \item Evaluate $\int\frac{x}{\sqrt{x^2 + 2x + 5}}\,dx$.
  \answerspace

  \end{enumerate}

\end{enumerate}

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