\chapter{Integration}

\section{Antiderivative}
\section{Integral}
\subsection{Riemann sum}
\section{Fundamental theorem of calculus}
\subsection{Linearity of the integral}
\subsection{Reverse chain rule}
\subsection{Reverse product rule}
\section{Integration techniques}

\subsection{Table of integrals}
Here is a table of standard integrals.
$\int \frac{f'(x)}{f(x)}dx = \ln|f(x)|+C$
$\int x^n dx = \frac{x^{n+1}}{n+1}+C$
$\int \cos(x) dx = \sin(x)+C$
$\int \sin(x) dx = -\cos(x)+C$
$\int e^x dx = e^x+C$
$\int a^x dx = \frac{1}{\ln(a)}a^x+C$
$\int \frac{1}{x} dx = \ln|x|+C$
$\int \sec^2 (x) dx = \tan(x)+C$
$\int \ln (x) dx = x\ln(x)-x+C$
$\int \tan (x) dx = -\ln|\cos(x)|+C$
$\int \sec(x) dx = \ln|\sec(x)+\tan(x)|+C$
$\int \frac{a}{a^2 +x^2} dx = \tan^{-1}(\frac{x}{a}) +C$
$\int \frac{1}{\sqrt{a^2 -x^2}} dx = \sin^{-1}(\frac{x}{a}) +C$
\subsection{$t$-formulae}
\subsection{Trigonometric substitution}
\subsection{Trigonometric manipulations}
\subsection{Recursive formulae}
\subsection{Partial fraction decomposition}