Question

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

Answer 1

\[\int\sqrt{x} \left( x^3 - \frac{2}{x} \right)dx\]
\[ = \int\left( x^\frac{7}{2} - \frac{2}{\sqrt{x}} \right)dx\]
\[ = \int\left( x^\frac{7}{2} - 2 x^{- \frac{1}{2}} \right) dx\]
`= x^(7/2+1) / (7/2+1)  - 2 (x^(-1/2+1))/(-1/2+1 )+ C`
\[ = \frac{2}{9} x^\frac{9}{2} - 4 x^\frac{1}{2} + C\]
\[ = \frac{2}{9} x^\frac{9}{2} - 4\sqrt{x} + C\]