Question

Find the integral

Answer 1

use \(u=\tan(x)\) so \(du=\sec^2(x)dx\) then write the other \(\sec^2(x)\) in terms of tangent

Answer 2

Adding.

You can re-write the integrand as, \(\color{#0000ff }{ \displaystyle \sqrt{\tan(x)}\cdot\left[\tan^2(x)+1\right]\cdot\left[\sec^2(x)dx\right] }\) ....