** Stefan-Boltzmann constant (20-60 min)

Calculate the numerical value of the Stefan-Boltzmann constant

$$\sigma=(k_BT/h)^4 8\pi^5/15c^3$$

using the Planck radiation law for $u(\nu,T)$. In the calculation, you need the integral $\int_{0}^{\infty}dx{x^3}/({e^x-1}) = {\pi^4}/{15}$ which you should try to prove.