CIE A Level Maths: Pure 3复习笔记5.1.3 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
• The type of fraction dealt with here is a specific case of Reverse Chain Rule

• “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