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Following are methods of finding integral that we have studied along with the necessary information we have to identify.  Given the integrals, find the appropriate method of integration and identify the relevant information for that method.  use numerical only when all other options fail. Assume $a$ and $b$ are constants.

\vspace{5mm}






\begin{tabular}{|c|c|}
\hline
Method&Information to Identify\\
\hline
Elementary integral&None (we can take integral directly)\\
\hline
Substitution&O.F.=$f(u)$;  I.F. = $u=f(x)$;   $du=f'(x)dx$\\
\hline
Integration by Parts& $u=$ \hspace{10mm}   $v'=$\hspace{10mm}   $u'=$\hspace{10mm}   $v=$\\
\hline
Integration by Partial Fractions&Decompose fraction into sum (Evaluating numerators is step 2)\\
\hline
Numerical Approximation&Must use $LEFT(n)$, $RIGHT(n)$, $MID(n)$, $TRAP(n)$, or $SIMP(n)$\\
\hline

\end{tabular}

\vspace{10mm}

\begin{tabular}{ccc}
Integral & \hspace{7mm} Method (2 pts each) \hspace{2mm} &Necessary Information for the method (3 pts each) \hspace{5mm} \\[10 pt]


$ \int_a^b \, \arctan 5x \, dx$&&\\[60 pt]


$ \int_a^b \, x^2 e^{x^3} \, dx$&&\\[60 pt]


$ \int_a^b \, \frac{1}{1+x^2} \, dx$&&\\[60 pt]


$ \int_a^b \, \frac{3x+1}{x^2-4} \, dx$&&\\[60 pt]


$ \int_a^b \, \frac{e^{x^2}}{x} \, dx$&&\\[60 pt]

\end{tabular}

\newpage

Following are methods of finding integral that we have studied along with the necessary information we have to identify.  Given the integrals, find the appropriate method of integration and identify the relevant information for that method.  use numerical only when all other options fail. Assume $a$ and $b$ are constants.

\vspace{5mm}






\begin{tabular}{|c|c|}
\hline
Method&Information to Identify\\
\hline
Elementary integral&None (we can take integral directly)\\
\hline
Substitution&O.F.=$f(u)$;  I.F. = $u=f(x)$;   $du=f'(x)dx$\\
\hline
Integration by Parts& $u=$ \hspace{10mm}   $v'=$\hspace{10mm}   $u'=$\hspace{10mm}   $v=$\\
\hline
Integration by Partial Fractions&Decompose fraction into sum (Evaluating numerators is step 2)\\
\hline
Numerical Approximation&Must use $LEFT(n)$, $RIGHT(n)$, $MID(n)$, $TRAP(n)$, or $SIMP(n)$\\
\hline

\end{tabular}

\vspace{10mm}

\begin{tabular}{ccc}
Integral & \hspace{7mm} Method (2 pts each) \hspace{2mm} &Necessary Information for the method (3 pts each) \hspace{5mm} \\[10 pt]


$ \int_a^b \, \ln x \, dx$&&\\[60 pt]


$ \int_a^b \, e^x \sin e^x \, dx$&&\\[60 pt]


$ \int_a^b \, \frac{1}{x^2-1} \, dx$&&\\[60 pt]


$ \int_a^b \, \frac{3x+2}{3x^2+4x-4} \, dx$&&\\[60 pt]


$ \int_a^b \, x^7 \sin x^4 \, dx$&&\\[60 pt]

\end{tabular}
\end{document}