How can I integrate $\sqrt{\tan x}+ \sqrt{\cot x}$?

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How can I integrate $$\sqrt{\tan x}+ \sqrt{\cot x}$$

What method should I approach with?

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Break it in $\sin x$ and $\cos x$. Then write $\sin x \cdot \cos x$ as $\sqrt{(1 - (\sin x -\cos x)^2)}$.

And then let $(\sin x - \cos x)$ as $t$.