# How To: Find the antiderivative of a function

This video shows you how to find the antiderivative of a function. By definition, the F(x) is an antiderivative of f(x) means F'(x) = f(x). The small f is a derivative of the capital F, and the capital F is an antiderivative of the small f. One method of solving is to guess and check: to make a guess and check to see if it is true in the equation. For example, F(x) = 10x + 4. To guess that F(x) = 5x2 + 4x and check would result in the following: F'x = 10x + 4. With any constant you want to add, the derivative will always be zero. So, you can add anyone you want. So, this is true for F(x) = 5x2 + 4x – 60. So, for any equation: F(x) = 5x2 +4x + c. Once you have found one, add a plus c to it. This will give you all the antiderivatives that exist for the equation.

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