#### Answer

$$\frac{{4{x^3}}}{3} + 2{x^2} + x + C$$

#### Work Step by Step

$$\eqalign{
& \int {{{\left( {2x + 1} \right)}^2}} dx \cr
& {\text{expanding the integrand}} \cr
& \int {\left( {4{x^2} + 4x + 1} \right)} dx \cr
& {\text{integrate by the power rule}} \cr
& = \frac{{4{x^{2 + 1}}}}{{2 + 1}} + \frac{{4{x^{1 + 1}}}}{{1 + 1}} + x + C \cr
& {\text{Simplify}} \cr
& = \frac{{4{x^3}}}{3} + \frac{{4{x^2}}}{2} + x + C \cr
& = \frac{{4{x^3}}}{3} + 2{x^2} + x + C \cr} $$