# 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

#### How do I integrate f’(x)/f(x)?

• “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

#### 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

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