What Is An Antiderivative?

In calculus, an antiderivative is a function that reverses what a derivative does. If you take a function, calculate its derivative, and then find the antiderivative of that result, you end up right back where you started.

The Mathematical Definition

Formally, a function F(x) is an antiderivative of f(x) if the derivative of F(x) is equal to f(x). In notation, this is written as F'(x) = f(x).

Why Do We Add "+ C"?

When you take the derivative of a constant number, the result is zero. Because of this, x^2, x^2 + 5, and x^2 - 42 all have the exact same derivative: 2x. Therefore, when we find the general antiderivative of 2x, we write it as x^2 + C, where C represents any constant number.

To see how this works in practice with various functions, try typing different equations into our interactive Antiderivative Calculator.