\(\int \left(\frac{\sqrt x}{2} + \frac2{\sqrt x}\right) dx = \frac12 \int \sqrt x dx + 2 \int x^{-\frac12}dx\)
\(= \frac12 \times \frac23 x^{\frac32} + 2 \times 2 x^\frac12 + C\)
\(= \frac13 x^\frac32+ 4 \sqrt x+ C\)
\(= \frac13 x\sqrt x + 4\sqrt x + C\)