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Integration by substitution simplifies an integral by replacing part of it with a new variable u, transforming it into a standard integral. This topic covers choosing a substitution and changing the limits. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Choose u, usually the inside of a bracket or a root, and find du in terms of dx. Replace every x, including in dx, so the integral is purely in u. For a definite integral, convert the limits to u values too rather than substituting back at the end.
Before you start
Check the reverse chain rule first if this feels hard. Examined in Pure 4. Expect to use it again in harder integrals in Pure 4. The topic sits within Integration.
What you learn
The course works through the substitution method, definite integrals: change the limits, trig & exponential substitutions and definite trig/exp 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
We teach Integration by Substitution as one of the Integration topics in our A-level course library, at the second year of A-level. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. It sits alongside Integration of f(ax+b), Integration of Standard Functions, Integration of Trig Functions and Integration of xⁿ in the same strand. Endless extra practice on this strand is available on the Integration revision engine, which generates a fresh question each time.
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