A-Level · Maths
Integration by parts
What is integration by parts?
Integration by parts is the integral analogue of the product rule: ∫ u dv/dx dx = uv − ∫ v du/dx dx. Use it whenever the integrand is a product of two functions where one becomes simpler under differentiation (typically polynomial × exponential, polynomial × trig, or x × log x). The LIATE rule helps pick u: Logarithm, Inverse trig, Algebraic, Trig, Exponential.
Where it appears in exams
- Evaluate ∫ x · e^x dx — pick u = x, dv/dx = e^x.
- Evaluate ∫ ln(x) dx — pick u = ln(x), dv/dx = 1.
- Definite-integral exam questions where IBP is signalled by an x · trig product.
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Related glossary terms
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