What is the general antiderivative of $f (x) = x {(4 - x)}^{2}$ $f(x) = x(4 − x)^2$ ?

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Answer 1 · 2015-02-23T20:35:41

Hello,

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

$F (x) = \frac{x^{4}}{4} - \frac{8}{3} x^{3} + 8 x^{2} + c$ $F(x) = (x^4)/4 - 8/3 x^3 + 8x^2 + c$

where $c$ $c$ is an arbitrary real constant.

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