Find the anti-derivative of LaTeX: \displaystyle f(x) = \frac{6 x^{3} + 2 x^{2} - 9 x + 9}{\sqrt[4]{x}}

Using termwise division gives LaTeX: \displaystyle f(x) = 6 x^{\frac{11}{4}} + 2 x^{\frac{7}{4}} - 9 x^{\frac{3}{4}} + \frac{9}{\sqrt[4]{x}} . Finding the antiderivative of each term gives LaTeX: \displaystyle F(x) = \frac{8 x^{\frac{15}{4}}}{5} + \frac{8 x^{\frac{11}{4}}}{11} - \frac{36 x^{\frac{7}{4}}}{7} + 12 x^{\frac{3}{4}} + C