indefinite integral

$${f}{\left({\mathtt{x}}\right)} = \left(\left({\mathtt{4}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{x}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{x}}}^{{\mathtt{2}}}\right)\right)$$

$$\\\int((4x^{0.5}-1.5)(2x^{-1}+x^2))dx\\\\ =\int((4x^{0.5})(2x^{-1}+x^2)-1.5(2x^{-1}+x^2))dx\\\\ =\int(8x^{-0.5}+4x^{2.5}-3x^{-1}-1.5x^2)dx\\\\ etc$$

Find the indefinite integral of the function f(x)=(4sqrt(x)-3/2)(2/x+x^2)

$$\\ \small{\text{ $f(x)= \left(4\sqrt{x}-\frac{3}{2}\right)\cdot \left(\frac{2}{x}+x^2\right) $}}\\\\ \small{\text{ $f(x)=4\sqrt{x} \cdot \frac{2}{x} + 4\sqrt{x} \cdot x^2 - \frac{3}{2} \cdot \frac{2}{x} - \frac{3}{2} \cdot x^2 $}}\\\\ \small{\text{ $f(x)=8 x^{\frac{1}{2}} \cdot x^{-1} + 4 x^{\frac{1}{2}} \cdot x^2 - 3 \cdot x^{-1} - \frac{3}{2} \cdot x^2 $}}\\\\ \boxed{ \small{\text{ $f(x)=8 x^{-\frac{1}{2}} + 4 x^{\frac{5}{2}} - 3 x^{-1} - \frac{3}{2} \cdot x^2 $}}}\\\\ \int{(8 x^{-\frac{1}{2}} + 4 x^{\frac{5}{2}} - 3 x^{-1} - \frac{3}{2} \cdot x^2 )}\ dx \\\\ \small{\text{ $ = 8\int{(x^{-\frac{1}{2}} ) }\ dx + 4\int{( x^{\frac{5}{2}} ) }\ dx - 3\int{( x^{-1} ) }\ dx - \frac{3}{2} \int{(x^2 ) }\ dx $ }}\\ \boxed{\int{(x^{-\frac{1}{2}} ) }\ dx = 2\sqrt{x} +c \qquad \int{(x^{ \frac{5}{2}} ) }\ dx = \frac{2}{7}x^3\sqrt{x} +c } \\ \boxed{\int{(x^{-1}) }\ dx = \ln{(x)} +c \qquad \int{(x^{2}) }\ dx = \frac{x^3}{3} +c } \\\\\\ \small{\text{ $ \int{(8 x^{-\frac{1}{2}} + 4 x^{\frac{5}{2}} - 3 x^{-1} - \frac{3}{2} \cdot x^2 )}\ dx =16\sqrt{x} + \frac{8}{7}x^3\sqrt{x} -3\ln{(x)} -\frac{x^3}{2} +c $ }}$$