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\centerline{MATH 134 -- Calculus with Fundamentals 2}
\centerline{Summary of Reduction Formulas for Trigonometric Integrals}
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\noindent
\begin{itemize}
\item (SC1)
$$\int \sin^n(u)\ du = \frac{-\sin^{n-1}(u)\cos(u)}{n} + \frac{n-1}{n} \int \sin^{n-2}(u)\ du.$$
\item (SC2)
$$\int \cos^n(u)\ du = \frac{\cos^{n-1}(u)\sin(u)}{n} + \frac{n-1}{n} \int \cos^{n-2}(u)\ du.$$
\item (SC3 and SC4)
\begin{align*}
&\int \sin^n(u)\cos^m(u)\ du \\
&=\begin{cases}
\displaystyle\frac{-\sin^{n-1}(u)\cos^{m+1}(u)}{n + m} + \frac{n-1}{n + m} \int \sin^{n-2}(u)\cos^m(u)\ du&\\
   &\\
\displaystyle \frac{\sin^{n+1}(u)\cos^{m-1}(u)}{n + m} + \frac{m-1}{n + m} \int \sin^n(u)\cos^{m-2}(u)\ du&
\end{cases}
\end{align*}
\item (ST1)
$$\int \tan^n(u)\ du = \frac{\tan^{n-1}(u)}{n-1} - \int \tan^{n-2}(u)\ du.$$
\item (ST2)
$$\int \tan(u)\ du = -\ln|\cos(u)| + C$$
\item (ST3)
$$\int \sec^n(u)\ du = \frac{\tan(u)\sec^{n-2}(u)}{n-1} + \frac{n-2}{n-1} \int \sec^{n-2}(u)\ du.$$
\item (ST4)
$$\int \sec(u)\ du = \ln|\sec(u) + \tan(u)| + C$$
\end{itemize}
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