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

For \(\alpha, \beta, \gamma, \delta \in N\), if
\[
\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _e x d x=\frac{1}{\alpha}\left(\frac{x}{e}\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{e}{x}\right)^{\delta x}+C
\]

Where \(e=\sum_{n=0}^{\infty} \frac{1}{n !}\) and \(C\) is constant of integration, then \(\alpha+2 \beta+3 \gamma-4 \delta\) is equal to:

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