Answer
$$\frac{{{u^4}}}{4} - {u^2} + 7u + C$$
Work Step by Step
$$\eqalign{
& \int {\left[ {{u^3} - 2u + 7} \right]} du \cr
& {\text{find the antiderivative by the power rule}} \cr
& = \frac{{{u^{3 + 1}}}}{{3 + 1}} - 2\left( {\frac{{{u^2}}}{2}} \right) + 7u + C \cr
& = \frac{{{u^4}}}{4} - {u^2} + 7u + C \cr} $$
