Indefinite integral

The infinitely many antiderivatives together form the indefinite integral. The general notation is:

$\int f(x)\,\mathrm{d}x=F(x)+C$

(read: the indefinite integral of f(x) with respect to x)

$\int$ is the integral symbol
$f(x)$ is the integrand
$x$ is the variable of integration
$C$ is the constant of integration

Info

$\mathrm{d}x$ is called the differential of the indefinite integral. It indicates that $x$ is the variable of integration, so the variable to be integrated.

All variables that do not occur in the differential are constants.

Remember

The indefinite integral of $f$ is the set of all antiderivatives of the function $f$.

Examples

$\int x^2\,\mathrm{d}x=\frac13x^3+C$

$\int 2x\,\mathrm{d}x=x^2+C$

$\int 4\,\mathrm{d}x=4x+C$