Edexcel A Level Maths: Pure:复习笔记8.2.4 f'(x)/f(x)
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
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.
Worked Example
转载自savemyexams
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