The value of \({\int }_{{\mathrm{e}}^{2}}^{{\mathrm{e}}^{4}}\frac{1}{\mathrm{x}}\left(\frac{{\mathrm{e}}^{{\left({\left(…

The value of \({\int }_{{\mathrm{e}}^{2}}^{{\mathrm{e}}^{4}}\frac{1}{\mathrm{x}}\left(\frac{{\mathrm{e}}^{{\left({\left({\log }_{\mathrm{e}}\mathrm{x}\right)}^{2}+1\right)}^{-1}}}{{\mathrm{e}}^{{\left({\left({\log }_{e}x\right)}^{2}+1\right)}^{-1}}+{\mathrm{e}}^{{\left({\left(6-{\log }_{e}x\right)}^{2}+1\right)}^{-1}}}\right)dx\) is

[JEE Main 2025, 23 Jan (Shift 1)]