Question:
Evaluate the following integrals:
$\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x$
Solution:
Assume $\sqrt{x}=t$
$d(\sqrt{x})=d t$
$\Rightarrow \frac{1}{2 \sqrt{x}} \mathrm{dx}=\mathrm{dt}$
$\Rightarrow \frac{1}{\sqrt{x}} \mathrm{dx}=2 \mathrm{dt}$
Substituting $\mathrm{t}$ and $\mathrm{dt}$
$\Rightarrow 2 \int \cos t d t$
$=2 \sin t+c$
But $\sqrt{x}=t$
$\Rightarrow 2 \sin (\sqrt{x})+c$
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