Question:
Evaluate: $\int \frac{\sec ^{2} \sqrt{x}}{\sqrt{x}} \mathrm{dx}$
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 $\int \frac{\sec ^{2} \sqrt{x}}{\sqrt{x}} d x$ we get,
$=\int 2 \sec ^{2} t d t$
$=2 \tan t+c$
$=2 \tan \sqrt{x}+c$
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