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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 4}\quad {\sl Feb. 11, 1999}

\begin{enumerate}
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\item Define the function $\arctan(x)$, including its domain and range, and
prove that $\frac{d}{dx} \arctan(x) = \frac{1}{x^2+1}$.
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\item Integrate $\int\frac{x}{\sqrt{3 - 2x - x^2}}\,dx$.
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\item Give the general form of the partial fraction decomposition of
\[
\frac{x^6+x^4+x^2+1}{(x-1)(x^2+3)^2(x+5)^3}
\]
(Do not solve for the constants).
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\item Integrate $\int \frac{x^3+1}{x(x^2+4)}\,dx$
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