Question

Evaluate

$\int \frac{{\sec }^2\sqrt{x}}{\sqrt{x}}dx$

Answer 1

$\int \frac{se{c}^2\sqrt{x}}{\sqrt{x}}dx$

Let $t=tan$ $\sqrt{x}$

$dt=\frac{se{c}^2\sqrt{x}}{2\sqrt{x}}dx$

(or) $2dt=\frac{se{c}^2\sqrt{x}}{\sqrt{x}}dx$

Hence the given integral becomes

$\int 2dt$

$=2t+c$

$=2tan\sqrt{x}+c$