Edexcel A Level Maths: Pure

Revision Notes

8.2.7 f'(x)/f(x)

A Level Only

Integrating fractions

  • The technique for integrating fractions depends on the type of fraction
  • For polynomial denominators see Integration using Partial Fractions
  • If dy/dx = 1/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 f’(x)/f(x)?

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

Exam Tip

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.

A Level Only

Worked Example

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

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