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  \textbf{Exam II} \\
  Math 166, Section A2
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\textbf{Useful Formulas:}
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\begin{eqnarray*}
  \frac{d}{dx} \tan(x) &=& \sec^2(x) \\
  \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 ${\displaystyle \int \frac{x^2}{x-1} \;dx}$
    \item ${\displaystyle \int} \sin^3(x) \cos^2(x) \;dx$
    \item ${\displaystyle \int \frac{2}{e^{-x}+1}\;dx}$
    \item ${\displaystyle \int x \ln(x)\;dx}$
    \item ${\displaystyle \int \frac{x^2+x+2}{x(x^2+1)}\;dx}$
    \item ${\displaystyle \int \frac{1}{x^2 \sqrt{16-x^2}}\;dx}$ using $x=4 \cos(\theta)$.
    \item ${\displaystyle \int \frac{x}{\sqrt{4-x^2}}\;dx}$ 
    \item ${\displaystyle \lim_{x \rightarrow 0} \frac{x^2}{\sin(x)}}$
    \item ${\displaystyle \int_0^1 \frac{1}{\sqrt{x}} \;dx}$
    \item ${\displaystyle \int x \sin(x^2) \;dx}$
  \end{enumerate}
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