> [!note] Formula > > $ > \int{f(g(x))g^\prime(x)}dx = \int{f(u)du} \quad \text{where} \quad u = g(x) > $ If $u = g(x)$ is a [[Derivative|differentiable]] [[Function|function]] whose range is on an interval $l$, and $f$ is continuous on $l$, then the [[Antiderivative|integral]] of the composite function $f(g)$ is: $ \int{f(g(x))g^\prime(x)}dx = \int{f(u)du} $ Since $ du = dg(x) = g^\prime(x)dx $ - See [[Math/Calculus/Derivative/Chain Rule|chain rule]].