# Antiderivative > [!Antiderivative] > An *antiderivative* of a function $f$ is a differentiable function $F$ whose derivative is $f$. That is, > $F'=f$ The process of finding an antiderivative is *antidifferentiation* and is the inverse of [[Derivative|differentiation]]. Antiderivatives are also known as [[Integral|indefinite integrals]], as there are an *infinite set* of them for every function, to distinguish them from *definite integrals*. They are the result of integrals with *unspecified bounds*. An arbitrary constant known as the *constant of integration* is required to express a set of antiderivatives. This constant arises from the fact that the derivative of a constant is *zero*. Antiderivatives are related to other core calculus concepts in the [[fundamental theorem of calculus]]. >[!Example]+ > For the function $f(x)=3x^{3}+4x^{2}$, its antiderivatives can be expressed as $F(x)=\frac{3}{4}x^{4}+\frac{4}{3}x^{3}+C$. > > Any function of the form $F(x)$ will differentiate into the function $f(x)$. > > All valid antiderivatives of the function are *vertical translations* of each other. Shown below are three of the infinite antiderivatives, where $C=-1,0,1$ > > ![[AntiderivativeExample.svg|300]]