Question:medium
$\displaystyle\int \frac{2\,dx}{(e^{x} + e^{-x})^{2}}$ is equal to
$\displaystyle\int \frac{2\,dx}{(e^{x} + e^{-x})^{2}}$ is equal to
Show Hint
$(e^x+e^{-x})^2 = e^{-2x}(1+e^{2x})^2$. Multiply numerator and denominator by $e^{2x}$ to set up a standard substitution.
Updated On: Apr 8, 2026
- $\dfrac{e^{2x}}{1+e^{2x}} + c$
- $\dfrac{e^{-2x}}{1+e^{-2x}} + c$
- $\dfrac{1}{1+e^{2x}} + c$
- $-\dfrac{1}{1+e^{2x}} + c$
Show Solution
The Correct Option is D
Solution and Explanation
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