Integration using Partial Fractions (CIE A Level Maths: Pure 3)

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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

 Notes pf_eg, AS & A Level Maths revision notes

How do I integrate using partial fractions?

  • Fractions with linear denominators can be integrated (See Integrating Other Functions)

Notes ln_eg, AS & A Level Maths revision notes

  • A fraction with a polynomial denominator (degree 2+) can be integrated by …
    • … splitting using partial fractions
    • … integrating each partial fraction

Notes pf_int1, A Level & AS Level Pure Maths Revision Notes Example pf_int2, AS & A Level Maths revision notes 

  • 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 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

Example soltn_a, A Level & AS Level Pure Maths Revision NotesExample soltn_b, AS & A Level Maths revision notesExample soltn_c, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.