A LevelMathsEdexcelPureRevision NotesIntegrationFurther IntegrationIntegrating f'(x)/f(x)

Integrating f'(x)/f(x) (Edexcel A Level Maths) : Revision Note

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Edexcel Maths: PureCambridge (CIE) Maths: Pure 3OCR Maths A: PureAQA Maths: Pure

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f'(x)/f(x)

Integrating fractions

  • The technique for integrating fractions depends on the type of fraction

  • For polynomial denominators see Integration using Partial Fractions

  • If fraction numerator d y over denominator d y end fraction space equals space 1 over x then y = ln |x| + c – see Integrating Other Functions

  • The type of fraction dealt with here is a specific case of Reverse Chain Rule

Notes diff_lnfx, AS & A Level Maths revision notes

How do I integrate fraction numerator straight f apostrophe left parenthesis x right parenthesis over denominator straight f left parenthesis x right parenthesis end fraction?

Notes top_diff_bot, A Level & AS Level Pure Maths Revision Notes

  • “The top is ‘almost’ the derivative of the bottom”

    • 'almost' here meaning 'a multiple of' (see below)

  • The integral will involve ln |f(x)| - ie ln of the bottom

    • Due to reverse chain rule

Notes f’_f_eg, AS & A Level Maths revision notes

Why ‘almost’? 

Notes f’_f_eg_adj_comp, AS & A Level Maths revision notes

  • There may be coefficients to ‘adjust’ and ‘compensate’ for

Examiner Tips and Tricks

  • If you're unsure if the fraction is of the form f’(x)/f(x), differentiate the denominator.

  • Compare this to the numerator but you can ignore any coefficients.

  • If the coefficients do not match then ‘adjust’ and ‘compensate’ for them.

Worked Example

Example soltn1, AS & A Level Maths revision notes
Example soltn2, AS & A Level Maths revision notes
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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

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.

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