\[
\int {\frac{1}{{x^{\frac{2}{3}} }}dx}  = \int {x^{ - \frac{2}{3}} dx}  = \frac{{x^{ - \frac{2}{3} + 1} }}{{ - \frac{2}{3} + 1}} = \frac{{x^{\frac{1}{3}} }}{{\frac{1}{3}}} = 3x^{\frac{1}{3}}  = 3\sqrt[3]{x}
\]