Problem: Consider the following integral:$I(\epsilon) = \int_0^{10} \frac{dx}{(\epsilon + 9x^5 + x^{11})^\frac{13}{7}}$In the limit$\epsilon \to 10^6$, find approximate behavior of the integral up to and including the first leading order in \epsilon. Provide your answer in a $\boxed{}$ latex environment.
Solution: $\boxed{I(\epsilon) = \frac{\sqrt[11]{-1 + 2^{\frac{7}{13}}}}{\epsilon^{\frac{136}{77}}}}$