If the integral \({\int }_{0}^{10}\frac{[\sin 2\pi x]}{{e}^{x-[x]}}dx=\alpha {e}^{-1}+\beta {e}^{-\frac{1}{2}}+\gamma\) …

If the integral \({\int }_{0}^{10}\frac{[\sin 2\pi x]}{{e}^{x-[x]}}dx=\alpha {e}^{-1}+\beta {e}^{-\frac{1}{2}}+\gamma\) where \(\alpha\), \(\beta, \gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\alpha+\beta+\gamma\) is equal to:

[JEE Main 2021, 17 Mar (Shift 2)]