Study Guide

# Indefinite Integrals - Integration by Partial Fractions

## 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.