Reverse Chain Rule (Cambridge (CIE) A Level Maths) : Revision Note
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Reverse Chain Rule
How do you integrate (ax + b)n?
The reverse chain rule can be used for integrating functions in the form y = (ax + b)n
Make sure you are confident using the chain rule to differentiate functions in the form y = (ax + b)n
The reverse chain rule works backwards
For n = 2 you will most likely expand the brackets and integrate each term separately
If n > 2 this becomes time-consuming and if n is not a positive integer we need a different method completely
To use the reverse chain rule
(provided n is not -1)
Raise the power of n by 1
Divide by this new power
Divide this whole function by the coefficient of x
You can check your answer by differentiating it
You should get the original function when you differentiate your answer
Note that this method only works when the function in the brackets is linear (ax + b)
Worked Example

Examiner Tips and Tricks
Make sure you can recognise when a question needs to use the reverse chain rule, it may not always be obvious.
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