Find the anti-derivative of LaTeX: \displaystyle f(x) = \frac{4 x^{3} + 8 x^{2} - 9 x - 2}{\sqrt[3]{x}}

Using termwise division gives LaTeX: \displaystyle f(x) = 4 x^{\frac{8}{3}} + 8 x^{\frac{5}{3}} - 9 x^{\frac{2}{3}} - \frac{2}{\sqrt[3]{x}} . Finding the antiderivative of each term gives LaTeX: \displaystyle F(x) = \frac{12 x^{\frac{11}{3}}}{11} + 3 x^{\frac{8}{3}} - \frac{27 x^{\frac{5}{3}}}{5} - 3 x^{\frac{2}{3}} + C