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4.7
Antiderivatives
Copyright © Cengage Learning. All rights reserved.

2. Antiderivatives
Following is the formal definition of antiderivative of f.
If F and G are any two antiderivatives of f, then
so , where C is a constant.

3. Antiderivatives
We can write this as , so we have the following result.

4. Antiderivatives
In Table 2 we list some particular antiderivatives.

5. Example 2 Find all functions g such that Solution:
We first rewrite the given function as follows:

6. Example 2 – Solution Thus we want to find an antiderivative of
cont’d
Thus we want to find an antiderivative of
Using the formulas in Table 2 together with Theorem 1, we obtain