Answer
$$6x - \frac{{{x^3}}}{3} + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {6 - {x^2}} \right)} dx \cr
& {\text{use multiple constant rule }}\int {k \cdot f\left( x \right)} dx = k\int {f\left( x \right)} dx \cr
& = \int 6 dx - \int {{x^2}dx} \cr
& {\text{use power rule }}\int {{x^x}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = 6\left( {\frac{{{x^{0 + 1}}}}{{0 + 1}}} \right) - \frac{{{x^{2 + 1}}}}{{2 + 1}} + C \cr
& {\text{simplifying}} \cr
& = 6\left( x \right) - \frac{{{x^3}}}{3} + C \cr
& = 6x - \frac{{{x^3}}}{3} + C \cr} $$