Cracking The Ap Calculus ab Exam 2018

Now use u-substitution: let u = and du = dx, so 2du = dx, and substitute.

When you substitute back, you get

sin−1   +   C

Example 6:

Again, use u-substitution. Let u = ex and du = ex dx, and substitute.

    =   tan−1 u +   C

Then substitute back.

tan−1ex +   C

Let’s do one last type that’s slightly more difficult. For this one, you need to remember how to complete
the square.

Example 7:

Complete the square in the denominator (your algebra teacher warned you about this).

x^2     +   4x  +   5   =   (x  +   2)^2    +   1

Now rewrite the integral.