Problem: Consider the following integral:$I(x) = \int_0^3 (\cos(t^2) + 5 + 2t^3) e^{-x(2e^t + 7 + \sin(t))} dt$In the limit$x\to\infty$, find approximate behavior of the integral up to and including the first leading order in x. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{y(x)= \frac{2e^{-9x}}{x}}$