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Integration by parts integrates a product of two functions by reversing the product rule: ∫u(dv/dx)dx = uv − ∫v(du/dx)dx. It handles integrals like x·eˣ, x·sin x and ln x that no other standard method can. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
The integral of u dv equals uv minus the integral of v du. Choose u as the part that gets simpler when differentiated — usually a power of x or a logarithm. Apply it twice if one pass leaves another product.
Before you start
Best tackled after the product rule and standard integrals. It is Pure 4 content. It reappears throughout integrals of products and logarithms. Filed under Integration.
What you learn
The course works through the method: choose, find, apply, repeated parts & the loop, definite integration by parts and applied & 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 by Parts belongs to Integration and is met in the second year of A-level. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Students often pair it with Integration by Substitution, Integration of f(ax+b), Integration of Standard Functions and Integration of Trig Functions. For unlimited practice, the Integration revision engine builds new questions on demand and records your accuracy.
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