How to integrateroot of tanx + root of cotx

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\\I=\int \sqrt{tan x}+\sqrt{cot x},\ \ \ Let\ tan\ x=t^2\\therefore\\2t\ dt=sec^2x dx=(1+tan^2)dx=(1+t^2)dx\\\\dx=\frac{2t}{1+t^2}\\\\ I= \int {(t+\frac{1}{t})\frac{2t}{1+t^2}} dt \\\\= \int{\frac{(t^2+1)}{t}\frac{2t}{1+t^2}} dt\\\\= \int{2} \, dt \\\\=2t+C\\\\=2\sqrt{tan\ x}+C\\
 

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