Show that in the first approximation the partition function of a system of (N) noninteracting, indistinguishable particles

Question:

Show that in the first approximation the partition function of a system of $N$ noninteracting, indistinguishable particles is given by

\[
Q_{N}(V, T)=\frac{1}{N ! \lambda^{3 N}} Z_{N}(V, T),
\]

where

\[
Z_{N}(V, T)=\int \exp \left\{-\beta \sum_{i\]

$v_{s}(r)$ being the statistical potential (5.5.28). Hence evaluate tht first-order correction to the equation of state of this system.