# Indefinite Integrals

# Integration by Partial Fractions

**Integration by partial fractions** is a technique we can use to integrate rational functions when the degree of the numerator is less than the degree of the denominator. Here's the big picture:

- We start out with an integral whose integrand is a rational function, like

The degree of the numerator must be less than the degree of the denominator.

- We do some sneaky stuff to rewrite the original rational function as a sum of
**partial fractions**:

- We integrate the partial fractions, whose antiderivatives all involve the natural log:

**Be Careful:** When *x* occurs in a denominator with a coefficient other than 1, you have to use integration by substitution.