Hướng dẫn giải

Ta có \(F\left( e \right) - F\left( 1 \right) = \int\limits_1^e {\frac{{\ln x}}{x}dx} = \int\limits_1^e {\ln xd\left( {\ln x} \right)} = \frac{{{{\ln }^2}x}}{2}\left| {_{\scriptstyle\atop\scriptstyle1}^{\scriptstylee\atop\scriptstyle}} \right. = \frac{1}{2}.\)