Integration using Partial Fractions (OCR A Level Maths A) : Revision Note
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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
Examiner Tips and Tricks
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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