If the value of the integral \(\int_0^5 \frac{x+[x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta\), where \(\alpha, \beta \in R, …

If the value of the integral \(\int_0^5 \frac{x+[x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta\), where \(\alpha, \beta \in R, 5 \alpha+6 \beta=0\), and \([x]\) denotes the greatest integer less than or equal to \(x\); then the value of \((\alpha+\beta)^2\) is equal to

[JEE Main 2021, 26 Aug (Shift 2)]