Global binding integral of the hypervirial model ($I=\frac{p+1}{p}\frac{\Gamma (1+1/p{)}^2}{\Gamma (2+2/p)}$)

In unit scales $I=\int \rho \psi d^{3}x=(p+1)\Gamma (1+1/p{)}^2/[p\Gamma (2+2/p)]$. The local virial relation of the hypervirial model gives global energies $T=I/4$ and $W=-I/2$. Restoring physical scales multiplies each integral by $G{M}^2/a$.