Answer
$\dfrac{1}{3} x^{3/2}+4 x^{1/2} dx+C$
Work Step by Step
Given: $\int (\dfrac{\sqrt x}{2}+\dfrac{2}{\sqrt x}) dx$
or, $\int (\dfrac{\sqrt x}{2}+\dfrac{2}{\sqrt x}) dx=\int\dfrac{1}{2} x^{1/2}+2 x^{-1/2} dx$
We have: $\int x^n dx=\dfrac{x^{n+1}}{n+1}+C$
Thus, $\int\dfrac{1}{2} x^{1/2}+2 x^{-1/2} dx=\dfrac{1}{3} x^{3/2}+4 x^{1/2} dx+C$
