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

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 then y = ln |x| + c – see Integrating Other Functions

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

How do I integrate ?

• “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

Why ‘almost’? 

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