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\begin{center}
\textbf{Sample Test II} \\
Math 166, Section A2
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\begin{center}
\textbf{Useful Formulas:}
\begin{eqnarray*}
\sin^2(x)+\cos^2(x)&=&1 \\
\tan^2(x)+1&=&\sec^2(x) \\
\cos^2(x)&=&\frac{1+\cos(2x)}{2} \\
\sin^2(x)&=&\frac{1-\cos(2x)}{2}
\end{eqnarray*}
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\begin{enumerate}
\item ${\displaystyle \int \frac{x^2+x-3}{x-2}}$
\item ${\displaystyle \int} \cos^2(3x) \;dx$
\item ${\displaystyle \int \frac{4x}{x^2+9}\;dx}$
\item ${\displaystyle \int \ln(x)\;dx}$
\item ${\displaystyle \int \frac{2x}{x^2-5x+6}\;dx}$
\item ${\displaystyle \int \frac{1}{x^2 \sqrt{16-x^2}}\;dx}$ using $x=4 \cos(\theta)$.
\item ${\displaystyle \int \frac{\cot(x)}{\sin^2(x)}\;dx}$ 
\item ${\displaystyle \lim_{x \rightarrow 0} \frac{x^2}{\sin(x)}}$
\item ${\displaystyle \int_3^5 \frac{1}{x-3} \;dx}$
\item ${\displaystyle \int \frac{1}{1-\sin(x)} \;dx}$
\end{enumerate}
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