# AP Calculus AB : Antiderivatives following directly from derivatives of basic functions

## Example Questions

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### Example Question #22 : Techniques Of Antidifferentiation

Given , find the general form for the antiderivative .

Explanation:

To answer this, we will need to FOIL our function first.

Now can find the antiderivatives of each of these three summands using the power rule.

(Don't forget )!

### Example Question #23 : Techniques Of Antidifferentiation

Compute the following integral:

Explanation:

Compute the following integral:

Now, we need to recall a few rules.

1)

2)

3)

4)

We can use all these rules to change our original function into its anti-derivative.

We can break this up into separate integrals for each term, and apply our rules individually.

The first two integrals can be found using rule 2

Next, let's tackle the middle integral:

Then the "sine" integral

And finally, the cosine integral.

Now, we can put all of this together to get:

Note that we only have 1 c, because the c is just a constant.

### Example Question #24 : Techniques Of Antidifferentiation

Solve:

Explanation:

The integral can be solved knowing the derivatives of the following functions:

Given that the integrand is simply the sum of these two derivatives, we find that our integral is equal to

Solve: