#### Answer

$\frac{x^{4}}{2}-\frac{2x^{3}}{9} + \frac{5x^{2}}{2}+C$

#### Work Step by Step

Start with function $2x^{3}-\frac{2}{3}x^2+5x$.
Use power rule for antiderivatives (antiderivative of $x^{n}$ is $\frac{x^{n+1}}{n+1}$) on each of the three terms. Since the terms are added, the antiderivatives are also added. Add constant to make it most general form. We arrive at the answer $\frac{x^{4}}{2}-\frac{2x^{3}}{9} + \frac{5x^{2}}{2}+C$.