*Integration by parts* is a technique for integrating a product of functions. It states that if \(u\) and \(v\) are functions, then \[\int u \frac{dv}{dx} \,dx = uv - \int v \frac{du}{dx} \,dx.\]

This follows by integrating the product rule for differentiation, \[\frac{d}{dx}(uv) = \frac{du}{dx}v + u\frac{dv}{dx}.\]