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The reverse chain rule integrates expressions of the form ∫f′(g(x))g′(x) dx by inspection — a fast alternative to substitution. This topic covers recognising and integrating these patterns. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Look for a function multiplied by something close to its own derivative. Guess the integral by undoing the chain rule, differentiate your guess to check, then adjust the constant in front to make it match.
Before you start
This builds directly on the chain rule and standard integrals. It then feeds into integration by substitution.
What you learn
When the chain rule was used to differentiate, we reverse it to integrate. If it is a constant multiple, adjust by that constant. The course works through powers of a function, exponentials, trig via the reverse chain rule and definite integrals & area. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Reverse Chain Rule is a Integration topic in the A-level syllabus, covered here at the second year of A-level. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Trapezium Rule, Volumes of Revolution, Area Between Two Curves and Area Under a Curve. You can drill this strand further on the Integration revision engine, with your accuracy saved to your skill tree.
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