CIE A Level Maths: Pure 3复习笔记5.1.7 Integration using Partial Fractions
Integration using Partial Fractions
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
Exam Tip
- 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.
Worked Example
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