Question

Integrate:
$\sqrt{1 + \tan x} \ dx$

Answer 1

$\int \sqrt{1 + \tan(x) } dx \\ \: \int \frac{ (\sqrt{1 + \tan(x) })( \sqrt{1 - \tan(x) } }{ \sqrt{1 - \tan(x) } }dx \\ \int \frac{ \sec(x) }{1 - \tan(x) } dx \\ \int \frac{1}{ \cos(x) - \sin(x) } dx \\ \frac{1}{ \sqrt{2} } \int \sec( \frac{\pi}{4} + x ) dx \\ \frac{1}{ \sqrt{2} } ( log( \tan( \frac{\pi}{4} + x) + \sin( \frac{\pi}{4} + x ) ) + c$

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Answer 2

Answer:

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