$$\displaystyle\int{ \frac{ 1 }{ { \cos }^{ 2 } x \sqrt{ 1+ \tan x } } }d x$$
$2\sqrt{\frac{\sin(x)+\cos(x)}{\cos(x)}}+С$
$\frac{1}{\sqrt{\frac{\sin(x)+\cos(x)}{\cos(x)}}\left(\cos(x)\right)^{2}}$
