11th Grade - Antiderivative

# 3 - Antiderivative

## Definition of an antiderivative

This part of the site is useful for the next page : the integrals.
The antiderivative (or antiderivative) of a function f, is a function F such as F' = f.
A function has many antiderivatives which all dissent from a constant C. Here are two example of antiderivatives of functions :
If you derivate the function F, you find f.
In general :

If u is a function, an antiderivative of is , and an antiderivative of is . For the calculation, you also have to know that the antiderivative of a sum of functions is equal to the sum of the antiderivatives of the functions, and that if alpha is a real number, an antiderivative of is .

## How to calculate an antiderivative

In the examples above, you simply apply the general formula of a antiderivative of a power of x. Below we are going to use the formulas of the exponential and logarithm functions, and to do this we 'll have to modify f.
Suppose , then we have . Above we managed to express f functions of u and its derivative. Thus finally :

Last example,

Suppose , then and hence : .

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The antiderivatives

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