A LevelMathsEdexcelPureRevision NotesIntegrationFurther IntegrationReverse Chain Rule

Reverse Chain Rule (Edexcel A Level Maths: Pure): Revision Note

Exam code: 9MA0

Written by: Paul

Updated on 23 June 2025

Reverse chain rule

What is the chain rule?

The Chain Rule is a way of differentiating two (or more) functions

Notes cr, AS & A Level Maths revision notes

In many simple cases the above formula/substitution is not needed

Notes cr_egs, AS & A Level Maths revision notes

The same can apply for the reverse – integration

How do I integrate using the reverse chain rule?

Notes rcr_egs, A Level & AS Level Pure Maths Revision Notes

In more awkward cases it can help to write the numbers in before integrating

STEP 1: Spot the ‘main’ function
STEP 2: ‘Adjust’ and ‘compensate’ any numbers/constants required in the integral
STEP 3: Integrate and simplify

Notes num_adj1, A Level & AS Level Pure Maths Revision Notes

Notes num_adj2, AS & A Level Maths revision notes

Examiner Tips and Tricks

If in doubt you can always use a substitution.
Differentiation is easier than integration so if stuck try the opposite, eg. sin and cos are linked (remember that minus!) so if integrating a sin function, start by differentiating the corresponding cos function.
Lastly, check your final answer by differentiating it.

Worked Example

Example soltn(a), AS & A Level Maths revision notes

Example soltn(b), AS & A Level Maths revision notes

Example soltn(c), AS & A Level Maths revision notes

Example note, AS & A Level Maths revision notes

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