Question

Integrate the function $\frac{\cos \sqrt{x}}{\sqrt{x}}$

Answer 1

Let $\sqrt{x}=t$
$\therefore \frac{1}{2\sqrt{x}}dx=dt$
$\Rightarrow \int \frac{\cos \sqrt{x}}{\sqrt{x}}dx=2\int \cos tdt$
$=2\sin t+C$
$=2\sin \sqrt{x}+C$