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$\int\sqrt{1-\tan x}~\mathrm{d}{x}.$ is an integral which I am not able to solve. I have restricted my ideas on trigonometric substitution but cannot conclude to an answer...will really appreciate if someone could help me out..or suggest an alternative method for the same ..

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    $\begingroup$ $$\sqrt{1-\tan x}\mapsto \frac{\sqrt{1-x}}{1+x^2}\mapsto \frac{\sqrt{x}}{1+(1-x)^2}\mapsto \frac{x^2}{1+(1-x^2)^2}$$ and partial fraction decomposition. $\endgroup$ – Jack D'Aurizio Nov 2 '18 at 5:06
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Substituting $u=\sqrt{1-\tan x}$ gives a pretty easy integral.

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  • $\begingroup$ Okay sir...will try this out and update soon.thank you. $\endgroup$ – user611339 Nov 2 '18 at 5:05

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