Question

Integrate $\int \frac{{\tan }^4\sqrt{x}{\sec }^2\sqrt{x}}{\sqrt{x}}dx$ with respect to $x$.

Answer 1

$\tan \sqrt{x}=t$
$\frac{{\sec }^2\sqrt{x}}{2\sqrt{x}}dx=dt$
$I=2\int t^{4}dt$
$=2\frac{t^5}{5}+C$

$=\frac{2}{5}{\tan }^5\sqrt{x}+C$