Cracking The Ap Calculus ab Exam 2018

Using u-substitution, let u = x + 2 and du = dx. Then do the substitution.

    =   tan−1 u +   C

When you put the function of x back in to the integral, it reads:

tan−1(x +   2)  +   C

Evaluating these integrals involves looking for a particular pattern. If it’s there, all you have to do is use
algebra and u-substitution to make the integrand conform to the pattern. Once that’s accomplished, the rest
is easy. These integrals will show up again when we do partial fractions. Otherwise, as far as the AP
Exam is concerned, this is all you need to know.

Try these solved problems, and don’t forget to look for those patterns. Get out your index card, and cover
the answers while you work.

PROBLEM 1. Find the derivative of y = sin−1

Answer: The rule is

The algebra looks like the following:

PROBLEM 2. Evaluate

Answer: First, you need to do a little algebra. Factor 4 out of the denominator.