Question

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

Answer 1

Hello,

Because `f(x) = x(16 - 8x + x^2) = x^3 - 8x^2 + 16x`, so any antiderivative of `f` is

`F(x) = (x^4)/4 - 8/3 x^3 + 8x^2 + c`

where `c` is an arbitrary real constant.