Problem: Find an approximation using asymptotic series of $I(x) = \int_{x}^{\infty}t^{4}e^{-3t^4}dt$ in the limit$x \rightarrow \infty$. Provide your answer in a $\boxed{}$ latex environment. Do not use \cdots to indicate that the series continue on. Just give the three terms and that's it
Solution: $\boxed{e^{-3x^4}\Bigl(\frac{x}{12}+\frac{1}{144x^3}-\frac{1}{576x^7}+\frac{7}{6912x^{11}}-\frac{77}{82944x^{15}}+\frac{385}{331776x^{19}}-\frac{7315}{3981312x^{23}}+\frac{168245}{47775744x^{27}}-\frac{168245}{21233664x^{31}}+\frac{5215595}{254803968x^{35}}-\frac{182545825}{3057647616x^{39}}\Bigr)}$