$ \text{If } \displaystyle \int_{0}^{10}\frac{[\sin 2\pi x]}{e^{,x-[x]}},dx ;=; \alpha e^{-1}+\beta e^{-1/2}+\gamma,\ \text{ where } \alpha,\beta,\gamma \text{ are integers and } [x] \text{ is the greatest integer } \le x,\ \text{then the value of } \alpha+\beta+\gamma \text{ is:} $