\(\int(\sqrt{\tan x}+\sqrt{\cot x}) d x\) =
1
\(\sqrt{2} \sin ^{-1}(\sin x-\cos x)+c\), where c is a constant of integration.
2
\(\frac{1}{\sqrt{2}} \sin ^{-1}(\sin x-\cos x)+c\), where c is a constant of integration.
3
\(\sin ^{-1}(\sin x-\cos x)+c\), where c is a constant of integration.
4
\(2 \sin ^{-1}(\sin x-\cos x)+c\), where c is a constant of integration.