What are Partial Fractions?
- This is the reverse process to adding (or subtracting) fractions
- The common polynomial denominator is split into factors
- Make sure you are familiar with the notes on Partial Fractions
How do I integrate using partial fractions?
- Fractions with linear denominators can be integrated
(See Integrating Other Functions)
- A fraction with a polynomial denominator (degree 2+) can be integrated by …
- … splitting using partial fractions
- … integrating each partial fraction
- STEP 1: Factorise denominator, if needed
- STEP 2: Express as partial fractions
- STEP 3: ‘Adjust’ and ‘compensate’ each term so it can be integrated
(See Reverse Chain Rule)
- STEP 4: Integrate each term (usually involves ln) and simplify
When there are several parts, read the whole question:
- An early part may be a “show that” involving partial fractions
- A later part may be to integrate the original fraction
If you can’t do, or get stuck on, the partial fractions bit of the question you can still use the “show that” result to help with the integration.