An Interesting Integral

My Scioly teammates sent this meme in our Discord group chat:

Here’s my reply:

$$\int \sqrt{\tan x}dx=\frac{\sqrt{2}}{4}\ln \left(\frac{\tan x-\sqrt{2\tan x}+1}{\tan x+\sqrt{2\tan x}+1}\right)+\frac{\sqrt{2}}{2}[\arctan (\sqrt{2\tan x}+1)+\arctan (\sqrt{2\tan x}-1)]+C$$

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