Problem: Find a single expression with the first three terms in the asymptotic series of I(x) = \int\limits_{0}^{x} \frac{\sin t}{t} \ dt in the limit $x \to \infty$. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(x)=\frac{\pi}{2} - \frac{\cos x}{x} + \frac{\sin x}{x^2}}$