### Home > APCALC > Chapter 3 > Lesson 3.4.2 > Problem 3-166

3-166.

What is the general antiderivative, , for each function below? Test your solution by verifying that

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An **antiderivative** of a function * *is a function

*whose derivative is*

*. That is*

The antiderivative of is

*. However, for the antiderivative of a function*

*, we use a capital letter*

*. For example, we write the antiderivative of*

*as*

*.*

Since there are an infinite number of antiderivatives that are different only by a constant term, called a “family,” we add a constant “” to represent all of them. This is known as the

**general antiderivative (**or simply the antiderivative

**)**.

For example: If , then

*and*

*are both antiderivatives of*

*This is why we write* .

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Don't forget the vertical shift

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Be careful of your signs! Don't forget the vertical shift

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