Find the most general antiderivative of the function. Use C for the constant of the antiderivative.

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = x(9 − x)^2
F(x)=?

u = 9 - x
x = 9 - u
dx = -du

x * (9 - x)^2 * dx =>
(9 - u) * u^2 * -du =>
(u - 9) * u^2 * du =>
(u^3 - 9u^2) * du

Integrate:

(1/4) * u^4 - 3u^3 + C =>
(1/4) * u^3 * (u - 12) + C =>
(1/4) * (9 - x)^3 * (9 - x - 12) + C =>
(-1/4) * (x + 3) * (9 - x)^3 + C