Partial fractions

What it does

Splits one fraction into simpler ones you can integrate, like 1/((x − 1)(x + 2)) into A/(x − 1) + B/(x + 2).

Check the degrees first

It only works when the top's degree is less than the bottom's. If it is not, divide first, then split what is left over.

One term per factor

Each linear factor gets a constant on top. A repeated factor (x − 1)² gets two terms, over (x − 1) and over (x − 1)². A quadratic that will not factor gets Ax + B on top.

Finding the constants

Multiply through by the whole denominator, then put in the x that makes each factor zero. Each one leaves a single unknown.