Problem: Consider the following integral:$I(\epsilon) = \int_0^{10} \frac{1}{(\epsilon + 4x^3 + 2x^9)^{3/2}} dx$In the limit$\epsilon \rightarrow \infty$, find approximate behavior of the integral up to and including the leading order in x. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(\epsilon) = \frac{1}{\epsilon^{3/2}} \cdot 10}$