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

## Example Questions

### Example Question #11 : Techniques Of Antidifferentiation      Explanation: ### Example Question #12 : Techniques Of Antidifferentiation      Explanation: ### Example Question #13 : Techniques Of Antidifferentiation      Explanation: ### Example Question #14 : Techniques Of Antidifferentiation      Explanation: ### Example Question #81 : Integrals      Explanation: ### Example Question #21 : Techniques Of Antidifferentiation      Explanation: ### 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 ### Example Question #25 : Techniques Of Antidifferentiation

Solve:  None of the other answers    None of the other answers

Explanation:

The integral is equal to and was given by the following rule: Using this rule becomes more clear when we rewrite the integral as Note that because none of the answer choices had the integration constant C along with the proper integral result, the correct choice was "None of the other answers." Always check after solving an indefinite integral for C! 