Why does Wien's displacement law predict infinite radiation energy?

[g.lemaitre]

Wein's displacement law is

E (T,ν) = = v³F (v/T)

This is from Omnes' book on QM

... Rayleigh, who apparently found the function F in June 1900. He used a standard result from classical statistical physics (the equality, or “equipartition” of energy among all the degrees of freedom) and applied it to the radiation oscillators. He found F to be a constant. The result is perfectly correct from the standpoint of classical physics but at the same time perfectly absurd because his expression predicts that the total radiation energy (E(T,v)dv is infinite.

He doesn't explain why the total radiation is infinite. I'd like to know why.

 

[mfb]

E is increasing with $\nu$, if you integrate $\nu$ from 0 to infinity to get the full energy content (as all frequencies are allowed) you will see that the integral diverges.