Question:
Evaluate: $\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x$.
Solution:
let $\sqrt{x}=t$
Differentiating on both sides we get,
$\frac{1}{2 \sqrt{x}} d x=d t$
$\frac{1}{\sqrt{x}} d x=2 \mathrm{dt}$
substituting it in $\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x$ we get,
$=\int 2 \cos t d t$
$=2 \sin t+c$
$=2 \sin \sqrt{x}+c$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.