Suppose we randomly pick $N$ points inside the unit hypercube in $\mathbb{R}^{N}$. What is the expected value of the volume of the convex hull (in any $\mathbb{R}^{N-1}$ containing the convex hull)?

For example, if $N=2$, we are asking about the average length of a line segment in a unit square. This can be shown to be $\frac{2+\sqrt{2}+ 5\ln(1+\sqrt{2})}{15}\approx 0.521$

Is there a method to compute this expected value in general?