Question

$\int \sqrt{x}\left(x^3-\frac{2}{x}\right)dx$

Answer 1

$$\begin{gathered} \int \sqrt{x}\left(x^3-\frac{2}{x}\right)dx \\ =\int \left(x^{\frac{7}{2}}-\frac{2}{\sqrt{x}}\right)dx \\ =\int \left(x^{\frac{7}{2}}-2x^{-\frac{1}{2}}\right)dx \\ =\frac{x^{{\displaystyle \frac{7}{2}}+1}}{{\displaystyle \frac{7}{2}}+1}-2\frac{x^{-{\displaystyle \frac{1}{2}}+1}}{-{\displaystyle \frac{1}{2}}+1}+C \\ =\frac{2}{9}{x}^{\frac{9}{2}}-4x^{\frac{1}{2}}+C \\ =\frac{2}{9}{\mathrm{x}}^{\frac{9}{2}}-4\sqrt{\mathrm{x}}+C \end{gathered}$$