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