Problem: Consider the following integral:$I(x) = \int_{x}^{\infty} e^{-at^b} dt$In the limit$x \to +\infty$, find approximate behavior of the integral up to and including the leading order in x. Provide an expression for the approximate behavior of the integral in a $\boxed{}$ latex environment.
Solution: $\boxed{\int_{x}^{\infty} e^{-a t^b} \, dt \sim \frac{e^{-a x^b}}{a b x^{b-1}}}$