I wish to numerically evaluate a function of the form
$$ P(v_0) = \frac{e^{\int_0^{v_0}F(v)dv}}{\int_{-\infty}^{+\infty}e^{\int_0^{v_1}F(v)dv}dv_1} $$
In the denominator is the normalization constant which gives me the trouble.
The function $F$ is given by
$F(v) = -v+\frac{1}{1+\frac{v}{e^v-1}}-\frac{1}{1+\frac{ve^v}{e^v-1}}$
I can compute the nominator numerically:
P[v0_] :=
Exp[NIntegrate[-v + 1/(1 + v/(-1 + E^v)) - 1/(
1 + (E^v v)/(-1 + E^v)), {v, 0, v0}]];
Plot[P[v0], {v0, -20, 20}]
but can't manage to do it with the normalization constant included.
Any suggestions?