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# At a Glance - 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

x2 – 2x – 3 = (x – 3)(x + 1).

### Sample Problem

We wouldn't use the method of partial fractions on

because the denominator factors into

x2 + 2x + 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.