Evaluate: `intsqrt(("cosec"x-cotx)/("cosec"x+cotx).(secx)/sqrt(1+2secx)`dx

Explanation

To evaluate the integral

\[ I = \int \frac{\sqrt{\csc x - \cot x}}{\csc x + \cot x} \cdot \sec x \cdot \frac{1}{\sqrt{1 + 2 \sec x}} \, dx, \]

we can follow these steps:

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