The integral \( \int \sqrt{\cot x} e^{\sqrt{\sin x}} \sqrt{\cos x} ...

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The integral \( \int \sqrt{\cot x} e^{\sqrt{\sin x}} \sqrt{\cos x} d x \) equals:
\( \mathrm{P}^{12 i} \)
(1) \( \frac{\sqrt{\tan x} e^{\sqrt{\sin x}}}{\sqrt{\cos x}}+C \)
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(2) \( 2 e^{\sqrt{\sin x}}+C \)
(3) \( -\frac{1}{2} e^{\sqrt{\sin x}}+C \)
(4) \( \frac{\sqrt{\cot x} e^{\sqrt{\sin x}}}{2 \sqrt{\cos x}}+C \)
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