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

Explanation

To evaluate the integral

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

we will follow a series of steps.

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