MHB Trig. Indefinite Integral

[juantheron]

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 Substution form

Help me

Thanks

 

[Sudharaka]

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 Substution form

Help me

Thanks

Hi jacks, :)

Just out of curiosity where did you found this integral? Just a guess but this integral might be expressed through elementary functions. I am not quite sure, but as far as I know one can use the Risch Algorithm to determine whether a function has an elementary antiderivative.

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