For α, β, γ, δ ∈ N, if ∫((x/e)^2 x+(e/x)^2 x) log_e x d x=1/(α)(x/e)^β x-1/(γ)(e/x)^δ x+C, where e=Σ_n=0^∞ 1/(n!) and C is constant of integration,…

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