# What is the general antiderivative of f(x) = x(4 − x)^2?

Because $f \left(x\right) = x \left(16 - 8 x + {x}^{2}\right) = {x}^{3} - 8 {x}^{2} + 16 x$, so any antiderivative of $f$ is
$F \left(x\right) = \frac{{x}^{4}}{4} - \frac{8}{3} {x}^{3} + 8 {x}^{2} + c$
where $c$ is an arbitrary real constant.