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This topic integrates functions of a linear argument, f(ax + b), by reversing the chain rule and dividing by the coefficient a, extending standard integrals to expressions like (2x+1)⁵, e^(3x) and sin(4x). 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
Integrate as though the bracket were a single variable, then divide by the coefficient of x inside it. This only works when the inside is linear — if it is anything more complicated, you need substitution instead.
Before you start
You will want integration of standard functions at your fingertips first. It is Pure 3 content. It then feeds into the reverse chain rule.
What you learn
The course works through powers of a linear function, exponentials, trig with a linear argument, reciprocal of a linear function 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
In our A-level maths courses, Integration of f(ax+b) belongs to Integration and is met in 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 Integration of Standard Functions, Integration of Trig Functions and Integration of xⁿ. You can drill this strand further on the Integration revision engine, with your accuracy saved to your skill tree.
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