Question

How do you find the most general antiderivative of the function `f(x) = x(8 - x)^2`?

Answer 1

`f(x) = x(8 - x)^2` multiply it out to get standard form for a polynomial, then antidifferentiate term by term.

`f(x) = x(8 - x)^2 = x(64-16x+x^2) = x^3 - 16x^2+ 64x`

Whose antiderivative is: `1/4 x^4 - 16/3 x^3 +32 x^2 + C`