# Integration by Partial Fractions

Use the partial fractions technique when you're asked to evaluate a rational function that

- has a lower degree in the numerator than in the denominator, and

- has a denominator that can be factored into distinct linear factors.

### Sample Problem

We can use the method of partial fractions on

because the numerator has degree 0, the denominator has degree 2, and the denominator factors into

*x*^{2} – 2*x* – 3 = (*x* – 3)(*x* + 1).

### Sample Problem

We wouldn't use the method of partial fractions on

because the denominator factors into

*x*^{2} + 2*x* + 1 = (*x* + 1)(*x* + 1).

These are not distinct linear factors.

Actually, it is possible to use the method of partial fractions on this example, but the setup is a bit more complicated. We'll stick to the simpler examples of integration by partial fractions.