#### Answer

$\frac{3}{5}x^{5/3}+\frac{2}{5}x^{5/2}+C$

#### Work Step by Step

Start with original function: $\int (\sqrt[3] {x^{2}} + x\sqrt x)dx$.
Rewrite radicals as fractional powers: $\int (x^{2/3}+x^{3/2})dx$.
Use power rule for antiderivatives to integrate each term: $\frac{x^{5/3}}{\frac{5}{3}}+\frac{x^{5/2}}{\frac{5}{2}}+C$.
Simplify fractions to arrive at answer: $\frac{3}{5}x^{5/3}+\frac{2}{5}x^{5/2}+C$.