Find the anti-derivative of LaTeX: \displaystyle f(x) = \frac{5 x^{3} - 3 x^{2} + 4 x + 3}{\sqrt[3]{x}}

Using termwise division gives LaTeX: \displaystyle f(x) = 5 x^{\frac{8}{3}} - 3 x^{\frac{5}{3}} + 4 x^{\frac{2}{3}} + \frac{3}{\sqrt[3]{x}} . Finding the antiderivative of each term gives LaTeX: \displaystyle F(x) = \frac{15 x^{\frac{11}{3}}}{11} - \frac{9 x^{\frac{8}{3}}}{8} + \frac{12 x^{\frac{5}{3}}}{5} + \frac{9 x^{\frac{2}{3}}}{2} + C