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

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