Problem: Find the first two terms in the asymptotic series of $I(x)=\int_0^{\pi/4} e^{-x(\tan{t}-\frac{t^3}{6})}\sqrt{1+\sin^2(t)}dt$ in the limit $x \to \infty$. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(x)=(1/x)(1-e^{-\frac{x \pi}{4}}) }$