Evaluation of $\int\sqrt\frac{1+\tan x}{\csc^2 x+\sqrt{\sec x}}dx$

Evaluation of $\displaystyle \int\sqrt\frac{1+\tan x}{\csc^2 x+\sqrt{\sec x}}dx$

I have Tried The Given Integral Using

$\displaystyle \tan x = \frac{2\tan \frac{x}{2}}{1-\tan^2 \frac{x}{2}}$ and $\displaystyle \cos x = \frac{1-\tan^2 \frac{x}{2}}{1-\tan^2 \frac{x}{2}}$ and $\displaystyle \sin x = \frac{2\tan \frac{x}{2}}{1+\tan^2 \frac{x}{2}}$

but Could not find anything in standard Substitution form

Help me

Thanks

• Do you know that it should be possible to do it in closed form of functions we know? – mickep Sep 9 '15 at 8:56