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This topic integrates algebraic fractions by first splitting them into partial fractions, turning an awkward integral into a sum of simple ln or standard integrals. 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
Split the fraction into partial fractions first, then integrate each piece. Each linear factor gives a natural logarithm, so the answer is usually a sum of logs, which the log laws will combine into one.
Before you start
It assumes you can handle partial fractions and log integration. It then feeds into harder rational integrals.
What you learn
The course works through integrating a partial-fraction sum, finding the partial fractions, definite integrals: exact logs, harder denominators and area under a rational curve. 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
Integration Using Partial Fractions is a Integration topic in the A-level syllabus, covered here at the second year of A-level. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Related topics students usually take next include Reverse Chain Rule, Trapezium Rule, Volumes of Revolution and Area Between Two Curves. For unlimited practice, the Integration revision engine builds new questions on demand and records your accuracy.
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