top of page
Integrating xⁿ reverses differentiation: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c for n ≠ −1. This topic covers the power rule for integration, integrating sums of terms and the constant of integration. 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
Raise the power by one, then divide by the new power. Rewrite roots and reciprocals as powers first. Add the constant of integration for an indefinite integral — the mark is there for it. The rule fails for a power of minus 1, which gives a logarithm instead.
Before you start
This builds directly on index laws and differentiation. Later work on indefinite and definite integrals assumes it. It belongs to the Pure 1 specification.
What you learn
There is no reverse product or quotient rule here — so expand a product and split a quotient into separate powers of x before integrating. In a “show that” question, present the rewriting clearly and reach the printed result. The course works through the integration power rule, negative & fractional indices, rewrite before integrating and show that & verify by differentiating. 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 xⁿ belongs to Integration and is met in the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. It sits alongside Integration Using Partial Fractions, Reverse Chain Rule and Trapezium Rule in the same strand. Endless extra practice on this strand is available on the Integration revision engine, which generates a fresh question each time.
Still need help with a topic?
bottom of page