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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{Trigonometric functions}


\subsubsection{Integrals of trig functions and their inverses}

Parts of this list are simply a re-writing of the basic formulas for the derivatives
of trigonometric functions as indefinite integrals. Other parts are much more
difficult integrals which take sophisticated techniques of integration to explain.
Some of those techniques you'll see this semester, but others will wait until
next semester. There are a few basic trig functions whose integrals are not
listed, but those are just the cosecant and the cotangent, which are similar
to the secant and tangent, and not used very often.

\begin{enumerate}
\item \[
\int \sin (x)dx=-\cos (x)+C\]
 
\item \[
\int \cos (x)dx=\sin (x)+C\]
 
\item \[
\int \tan (x)dx=\ln |\sec (x)|+C\]

\item \[
\int \sec (x)dx=\ln |\sec (x)+\tan (x)|+C\]

\item \[
\int \frac{1}{\sqrt{1-x^{2}}}dx=\sin ^{-1}(x)+C=\arcsin (x)+C\]
 
\item \[
\int \frac{1}{1+x^{2}}dx=\tan ^{-1}(x)+C=\arctan (x)+C\]
 
\item \[
\int \frac{1}{|x|\sqrt{x^{2}-1}}dx=\sec ^{-1}(x)+C\]
 \end{enumerate}

\end{document}
