Question:

$$\int \frac{x^2 - 2x + 3}{\sqrt{x}} dx = \int (x^{3/2} - 2x^{1/2} + 3x^{-1/2}) dx = \frac{x^{5/2}}{5/2} - \frac{2x^{3/2}}{3/2} + \frac{3x^{1/2}}{1/2} + C = \frac{2}{5}x^{5/2} - \frac{4}{3}x^{3/2} + 6x^{1/2} + C$$