$\frac{1}{\sqrt{2}} (\arctan(\frac{\sqrt{2\tan x}+1}{1}) + \arctan(\frac{\sqrt{2\tan x}-1}{1})) + \frac{1}{2\sqrt{2}} \ln|\frac{\tan x + \sqrt{2\tan x} + 1}{\tan x - \sqrt{2\tan x} + 1}| + C$

$\frac{2}{3} (\tan x)^{3/2} + C$

$\frac{1}{2} \sqrt{\tan x} + C$

$\ln|\sqrt{\tan x}| + C$