Question

Solve: $\int \frac{\sin \sqrt{x}}{\sqrt{x}}dx$

Answer 1

$\int \frac{\sin \sqrt{x}}{\sqrt{x}}dx$

Let $\sqrt{x}=t⟹x=t^2⟹dx=2tdt$

$⟹\int \frac{\sin t}{t}2tdt2\int \sin tdt-2\cos t-2\cos \sqrt{x}+c$