# Integration by parts

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, $\frac{d}{dx}(uv) = \frac{du}{dx}v + u\frac{dv}{dx}.$