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\begin{document}

   \begin{center}
     {\bf MTH112 -- TEST 3}
   \end{center}

\begin{flushright}
   Name: \rule[0in]{1.5in}{.01in}
\end{flushright} \vs

\noin HONOR CODE: On my honor, I have neither given nor received 
any aid on this examination. \\
Signature: \rule[0in]{1.5in}{.01in}

\noin Note: Show all work on exam in order to receive full credit. 

\begin{enumerate}
\item  Integrate:
	\begin{enumerate}
	\item $\ds \int_3^7 \frac{1}{(x+1)(x-2)} \; dx $
	\vspace{2cm}\item $\ds  \int \frac{1}{x(x+1)(x+2)} \; dx $
	\vspace{2cm}\item $\ds \int \frac {x}{(x-3)(x+2)^2} \; dx $
	\vspace{2cm}\item $\ds \int \frac{5x^2+3x-2}{x^3+2x^2} \; dx $
	\end{enumerate}

\newpage
\item Integrate:
	\begin{enumerate}
	\item $\ds \int x \sqrt{4-x^2} \; dx $
	\vspace{2cm}\item $\ds \int \sqrt{3-2x-x^2} \; dx $
	\vspace{2cm}\item $\ds \int \frac{\sqrt{9x^2-4}}{x}\; dx $
	\vspace{2cm}\item $\ds \int \frac{x}{(x^2+4)^{5/2}} \; dx$
	\end{enumerate}

\newpage
\item Integrate:
	\begin{enumerate}
	\item $\ds \int \sin x + x^5  \; dx $
	\vspace{2cm}\item $\ds \int \frac{1+\sqrt{x+4}}{x} \; dx $
	\vspace{2cm}\item $\ds \int \pi \sin x + \cos(1/2) \tan(\pi x) \; dx $
 	\vspace{2cm}\item $\ds \int (1+\sqrt{x})^2 \; dx$
        \end{enumerate}

\newpage
\item  Integrate:
	\begin{enumerate}
    	\item $\ds \int \frac{1}{x-\root 3 \of {x}}\;dx$
	\vspace{2cm}\item $\ds \int_1^3 \frac{\sqrt{x-1}}{x+1} \; dx$
	\vspace{2cm}\item $\ds \int \frac{1}{\sqrt{1+\sqrt{x}}} \; dx$
	\vspace{2cm}\item $\ds \int \frac{\root 3 \of {x} +1}
			{\root 3 \of {x} -1} \; dx$
 	\end{enumerate}

\newpage
\item
	\begin{enumerate}
	\item Factor $x^4+1$ as the difference of squares by first adding
	add subtracting the same quantity. Use this factorization to
	evaluate: \[\int \frac{1}{x^4+1}\;dx\]
	\vspace{2cm}\item Integrate: \[\int e^x \cos(3x+4) \;dx\] 
	\vspace{2cm}\item Write out the form of the partial fraction
	decomposition for this function: --- do {\em not} determine the numerical values
	of the cofficients: \[\frac{1}{x^6-x^3}\]
	\vspace{2cm}\item Find the limit:\[\lim_{x\rightarrow \infty}\;
		\frac{\ln\ln x }{ \sqrt{x} }\]
	\end{enumerate}
 
\end{enumerate}
\end{document}




