# Evaluate the following integrals. intfrac{e^x+e^{-x}}{e^x-e^{-x}}dx

Evaluate the following integrals.
$\int \frac{{e}^{x}+{e}^{-x}}{{e}^{x}-{e}^{-x}}dx$
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$\text{To evaluate}$
$I=\int \frac{{e}^{x}+{e}^{-x}}{{e}^{x}-{e}^{-x}}dx$

$\text{Differentiating both sides}$
$\left({e}^{x}+{e}^{-x}\right)dx=dt$
$I=\int \frac{{e}^{x}+{e}^{-x}}{{e}^{x}-{e}^{-x}}dx$
$I=\int \frac{1}{t}dt$
$I=\mathrm{ln}\left(t\right)+C$
$I=\mathrm{ln}\left({e}^{x}-{e}^{-x}\right)+C$