Math Indefinite integrals Indefinite integral

# 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
i

### 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.
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### Remember

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

### Examples

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

• $\int 2x\,\mathrm{d}x=x^2+C$

• $\int 4\,\mathrm{d}x=4x+C$