- 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
- There may be coefficients to ‘adjust’ and ‘compensate’ for
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.