2.12.23 Asymptotic analysis

Condition: Write an asymptotic representation of the function given by the integral. The asymptotic representation must be extended to a term that is an infinitesimal function of \( x \rightarrow a \). \[ F(x)=\int_{x}^{+\infty} \frac{e^{-2 t}}{\sqrt{t+1}} d t, \quad x \rightarrow+\infty \]