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Answer
$$ \displaystyle\int \dfrac{\sqrt{\cot\left(x\right)}-\sqrt{\tan\left(x\right)}}{\sqrt{2}{\cdot}\left(\cos\left(x\right)+\sin\left(x\right)\right)}\, \mathrm d x = \color{red}{\text{ integral could not be found. }} $$
Explanation
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