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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
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\section{Using Tables of Integrals and Computer Algebra Systems}

\subsubsection{Tables of Integrals\label{tables of integrals}}

You can make use of a \hyperref{table of integrals}{}{}{%
TAB_INTEGRALS.TEX#table of integrals} when confronted by an integral that is
difficult to evaluate by hand. It should be remembered that integrals do not
often occur in exactly the form of those given in the table. It is usually
necessary to apply methods of integration, such as substitution or
integration by parts, to the integral in order to transform it into a form
given in the table.

\subsubsection{Computer Algebra Systems\label{computer algebra systems}}

These are systems such as Maple, Mathematica, and Derive, and Scientific
Notebook which incorporates the Maple engine. The computer algebra system
(or CAS) can perform substitutions that transform a given integral into one
that occurs in its stored formulas. There are a few things to remember when
integrating an indefinite integral with a CAS:

\begin{enumerate}
\item  Computer algebra systems omit the constant of integration.

\item  Absolute value signs are omitted in the answer.
\end{enumerate}

\begin{example}
$\int \frac{1}{3x-2}dx=\frac{1}{3}\ln \left| 3x-2\right| +C$ when integrated
by hand. The computer algebra systems Derive, Maple, and Mathematica all
give the answer $\frac{1}{3}\ln \left( 3x-2\right) $.
\end{example}

\subsection{Related Reference Topics}

{\small \hyperref{Table of integrals}{}{}{TAB_integrals.tex}}

\subsection{Related Scientific Notebook Topics}

{\small \hyperref{Calculus, change variable}{}{}{../../Help/DM7-5.tex#Change
of variables}}

{\small \hyperref{Calculus, integrate by parts}{}{}{%
../../Help/DM7-5.tex#Integration by parts}}

{\small \hyperref{Calculus, partial fractions}{}{}{%
../../Help/DM7-5.tex#Partial fractions}}

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