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Mathematics · JEE | INTEGRALS

हिन्दी

Find \( \int \frac{e^{2x} - 1}{e^{2x} + 1} \, dx \).

  1. A
    \( 2 \log |e^x + 1| + C \)
  2. B
    \( \log |e^{2x} + 1| + C \)
  3. C
    \( \log |e^x + e^{-x}| + C \)
  4. D
    \( \log |e^x - e^{-x}| + C \)
View Answer & Solution

Correct answer · Option C

\( \log |e^x + e^{-x}| + C \)

Explanation

Divide numerator and denominator by \( e^x \) to get \( \int \frac{e^x - e^{-x}}{e^x + e^{-x}} dx \). Putting \( e^x + e^{-x} = t \), the integral evaluates to \( \log |e^x + e^{-x}| + C \).
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