Problem: Consider the following integral:$ I(x) = \int_{x}^{\infty} K_0(t) \, dt $In the limit$x \to +\infty$, find approximate behavior of the integral up to and including the leading order in x. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(x) \sim \sqrt{\frac{\pi}{2x}} e^{-x}}$