Determine the value of $\int_{0}^{1} \frac{1}{1+x^3} dx$ is not elementary, but consider the integral $\int_{0}^{\infty} \frac{dx}{1+x^n}$ for $n=3$. Which identity relates this to the Beta function $B(x, y) = \int_{0}^{1} t^{x-1}(1-t)^{y-1} dt$?