Prove

Let $\sqrt{x}=t$

$\therefore \frac{1}{2 \sqrt{x}} d x=d t$

$\Rightarrow \int \frac{\cos \sqrt{x}}{\sqrt{x}} d x=2 \int \cos t d t$

$=2 \sin t+\mathrm{C}$

$=2 \sin \sqrt{x}+\mathrm{C}$