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This topic integrates the standard functions whose integrals must be known — eˣ, 1/x giving ln|x|, sin x, cos x and sec²x — the reverse of the standard derivatives. 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
Learn the standard integrals as the reverse of the derivatives: e to the x integrates to itself, 1 over x gives ln of the modulus of x, cos x gives sin x, sin x gives minus cos x. The sign on the last one is the one people drop.
Before you start
Bring differentiation of standard functions with you. It is Pure 3 content. Later work on reverse chain rule and substitution assumes it.
What you learn
Evaluate between limits for an exact value — often the area under a standard-function curve, or between two of them. The course works through the exponential & reciprocal, basic trig integrals, the wider trig set, combining standard functions 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 Standard Functions 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. Nearby topics in the same strand are Integration of Trig Functions, Integration of xⁿ, Integration Using Partial Fractions and Reverse Chain Rule. You can drill this strand further on the Integration revision engine, with your accuracy saved to your skill tree.
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