I'm having problems calculating this integral.
$$\int\frac{\text{d}x}{\sqrt{\tan(x)}}$$
I don't even know where to begin...
Thanks
2026-04-06 19:53:32.1775505212
How do I calculate integral of $\int\frac{\text{d}x}{\sqrt{\tan(x)}}$
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HINT:
$$2\sqrt{\cot x}=\sqrt{\cot x}+\sqrt{\tan x}+\sqrt{\cot x}-\sqrt{\tan x}=\dfrac{\cos x+\sin x}{\sqrt{\cos x\sin x}}+\dfrac{\cos x-\sin x}{\sqrt{\cos x\sin x}}$$
As $\int(\cos x+\sin x)dx=\sin x-\cos x,$ choose $\sin x-\cos x=u$ for the first integral.
May I leave for you the second integral?