$\int\sqrt{1-\tan x}~\mathrm{d}{x}.$ (Integral of a trigonometric function under square root)

Question

$\int\sqrt{1-\tan x}~\mathrm{d}{x}.$ is an integral which I am not able to solve. I have restricted my ideas on trigonometric substitution but cannot conclude to an answer…will really appreciate if someone could help me out..or suggest an alternative method for the same ..

Answer 1

Substituting $u=\sqrt{1-\tan x}$ gives a pretty easy integral.