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

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 .


    Don't forget the vertical shift .


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