#### Answer

$$F(x)= 6x^2+\frac{1}{3}x^3+C$$

#### Work Step by Step

Given $$f(x) =x(12+x)=12x+x^2$$
Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$
\begin{align*}
F(x) &=\frac{12x^2}{2}+\frac{x^3}{3}+C\\
&= 6x^2+\frac{1}{3}x^3+C
\end{align*}
To check
\begin{align*}
F'(x) &=12x+x^2\\
&=f(x)
\end{align*}