MathLiveIntegration by parts
Rewrites the integral of a product of two functions in terms of a simpler integral, by differentiating one factor and integrating the other. It is used when the integrand is a product such as x times an exponential or logarithm.
\int u\,dv = uv - \int v\,duWhat the symbols mean
| a differentiable function of x chosen from the integrand | |
| an antiderivative of dv, so v' = dv/dx | |
| the differential of u, du = u'(x)\,dx | |
| the remaining part of the integrand, the differential of v |
About this formula
- FieldMathematics
- TopicIntegral calculus
- LevelUniversity
- Also calledintegration by parts formula, IBP, parts integration, integral of product, tabular integration, integration by parts rule
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