Math 22 Antiderivatives and Indefinite Integrals

Antiderivatives

 A function $F$ is an antiderivative of a function $f$ when for every $x$ in the domain of $f$, 
 it follows that $F'(x)=f(x)$

 The antidifferentiation process is also called integration and is denoted by $\int$ (integral sign).
 $\int f(x)dx$ is the indefinite integral of $f(x)$

 If $F'(x)=f(x)$ for all $x$, we can write:
 $\int f(x)dx=F(x)+C$ for $C$ is a constant.

Basic Integration Rules

$1.\int kdx=kx+C$ for $k$ is a constant.

$2.\int kf(x)=k\int f(x)dx$

$3.\int [f(x)+g(x)]dx=\int f(x)dx+\int g(x)dx$

$4.\int [f(x)-g(x)]dx=\int f(x)dx-\int g(x)dx$

$5.\int x^{n}dx={\frac {x^{n+1}}{n+1}}+C$ for $n\neq -1$

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