For \(\alpha ,\beta ,\gamma ,\delta \in N\), if \(\int \left({\left(\frac{x}{e}\right)}^{2x}+{\left(\frac{e}{x}\right)}^…

For \(\alpha ,\beta ,\gamma ,\delta \in N\), if \(\int \left({\left(\frac{x}{e}\right)}^{2x}+{\left(\frac{e}{x}\right)}^{2x}\right){\log }_{e}xdx=\frac{1}{\alpha }{\left(\frac{x}{e}\right)}^{\beta x}-\frac{1}{\gamma }{\left(\frac{e}{x}\right)}^{\delta x}+C\) where \(e=\sum _{n=0}^{\infty }\frac{1}{n!}\) and C is a constant of integration, then \(\alpha +2\beta +3\gamma -4\delta\) is equal to:

[JEE Main 2023, 10 Apr (Shift 2)]