Indefinite integral

The notation $\int f(x)\,dx$ for the entire family of antiderivatives of $f$ .

The indefinite integral $\int f(x)\,dx$ denotes the complete family of antiderivatives of $f$ : if $F$ is one antiderivative, $\int f(x)\,dx = F(x)+C$ . Unlike a definite integral (a number), the indefinite integral is itself a function — or rather, a family of functions differing by a constant.

Examples

$\int 2x\,dx = x^2+C$ .
$\int e^x\,dx = e^x+C$ .