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Math

Attribution

Some of the content of this guide was modeled after a guide published by OpenStax and has been adapted for the NWP Learning Commons in January 2023. This work is licensed under a Creative Commons BY 4.0 International License.

Antiderivative

Antiderivative

Definition:

A function F is called an antiderivative of f on an interval I if F(x)=f(x) for all x in I

 

If we can find a function F(x) whose derivative is a known function f(x), then we can state F(x) is an antiderivative of the function f(x).

Examples of antiderivatives:

Antiderivative:  F(x) Derivative of Antiderivative:  ddxF(x) Function:  f(x)
C 0 0
1n+1xn+1+C n+1n+1xn+11+0 xn
sinx+C cosx+0 cosx
cosx+C (sinx)+0 sinx
tanx+C sec2x+0 sec2x
ex+C ex+0 ex
ln|x|+C 1x+0 1x
arcsinx+C 11x2+0 11x2
arctanx+C 11+x2+0 11+x2