2 min readβ’april 26, 2020

Catherine Liu

**Enduring Understanding FUN-6:**Recognizing opportunities to apply knowledge of geometry and mathematical rules can simplify integration.

**Essential Knowledge FUN-6.F.1:**Some rational functions can be decomposed into sums of ratios of linear, non-repeating factors to which basic integration techniques can be applied.

Let's consider the following integral:

The integrand is a rational function with two linear factors in the denominator. With our current techniques, we canβt solve this integral. However, by using partial fractions, we can split the rational integrand into two separate fractions that we know how to handle.

For the AP Calculus BC exam, you will only be dealing with examples where the denominator can be factored into non-repeating linear factors. A non-repeating linear factor is a term of the form (Ax+B) where A and B are numbers, and each term only shows up once in the denominator.

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