Integral does not evaluate as it should!

I have this integral, it must result in all the constant values ​​and the integral value in itself, which is Zeta[2/3] it can be done.

Erase everything["Global`*"]

e0 = (3 * h ^ 2) / (8 * m * L ^ 2)
ee = e0 * n ^ 2
ef = n ^ 3 / e0;

be[e_] : = 1 / (Exp[e/(k*t) - u/(k*t)] - 1);
g[e_] : = Reporter[(2/Sqrt[Pi]) * ((2 * Pi * m) / h ^ 2) ^ (3/2) * v * Sqrt[e]];

sub1 = {e / (k * t) -> x}
sub2 = {e -> x * k * t}

be[e] /. sub1;
g[e] /. sub2;

F[x_] : = Refine[(G[(G[(g[(g[e] /. sub2) * (be[e] /. sub1), assumptions -> {u == 0}

To integrate[f[x], {x, 0, Infinity}]