\int [5x^{2}+\frac{2}{x^{4}}-3\sqrt[3]{x}]dx = 5\int x^{2}dx+2\int x^{-4}dx-3\int x^{\frac{1}{3}}dx=5\frac{x^{3}}{3}+2\frac{x^{-3}}{-3}-3\frac{x^{\frac{4}{3}}}{\frac{4}{3}}+C= \frac{5x^{3}}{3}-\frac{2}{3x^{3}}-\frac{9\sqrt[3]{x^{4}}}{4}+C\