Problem: Write the first two term asymptotic series of $I(x) = \int^\infty_x \frac{e^{-t^2}}{1+t^5} dt$ in the limit $x \rightarrow \infty$. Do not approximate the denominator. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(x) = e^{-x^2}(\frac{1}{2x(1+x^5)} - \frac{(1+6x^5)}{4x^3(1+x^5)^2})}$