Question:
Evaluate: $\int \frac{\sin \sqrt{x}}{\sqrt{x}} \mathrm{dx}$
Solution:
let $\sqrt{x}=t$
Differentiating on both sides we get,
$\frac{1}{2 \sqrt{x}} d x=d t$
$\frac{1}{\sqrt{x}} d x=2 d t$
substituting it in $\int \frac{\sin \sqrt{x}}{\sqrt{x}} d x$ we get,
$=\int 2 \sin t d t$
$=-2 \cos t+c$
$=-2 \cos \sqrt{x}+c$