Question:medium

If \( \int \frac{dx}{\sqrt{e^{-2x} - 1}} \) is equal to :

Show Hint

Whenever an integral contains terms like \( e^{-x} \) or \( e^{-2x} \) inside a radical or denominator, multiplying the numerator and denominator by a suitable power of \( e^x \) often clears the negative exponents and reveals a straightforward substitution.
  • \( \sin^{-1} e^{-x} + C \)
  • \( \log|e^{-x} + \sqrt{e^{-2x}-1}| + C \)
  • \( \sin^{-1} e^x + C \)
  • \( \log|e^{-x} - \sqrt{e^{-2x}-1}| + C \)
Show Solution

The Correct Option is C

Solution and Explanation

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