Ans : (C)
Hint \(: \int_{\log _{e}{ }^{2}}^{x}\left(e^{x}-1\right)^{-1} d x=\log _{e}{ }^{\frac{3}{2}} \int_{\log _{e}{ }^{2}}^{x} \frac{e^{-x}}{1-e^{-x}} d x=\log _{e} \frac{\frac{3}{2}}{2}\)
$$
\mathrm{e}^{-\mathrm{x}}=\frac{1}{4} \mathrm{x}=\ln 4
$$