Special Case Antiderivatives
The same special cases that you had to memorize the derivatives of (i.e., trig functions, ), will now be the antiderivatives you must also have memorized. If you put the work in earlier in the AP Calc course memorizing your derivative special cases, that will pay off for you big right now as you are just undoing (taking the antiderivative of) those same derivative special cases.
Similar to your derivative special cases, your antiderivative special caseshave a base case , what happens when it is just a basic x inside the function. Once that base case has more than just an x inside it , you will need to perform an additional antiderivative process. The great part about antiderivatives on the AP Calc AB exam is that there is only one option for what that additional antiderivative process will be, a u-substitution . The u-substitution method is how you undo (take the antiderivative of) what was a Chain Rulederivative. You will learn the u-substitution method after you learn all of your Special Cases.
Like with all antiderivatives, the mechanics of a Definite Integral and an Indefinite Integral are the exact same. It is always what you do after you perform the antiderivative mechanics that makes the difference between the two methods.