The equation of state for dilute gases consisting of fermions or bosons is derived as a series expansion of the pressure in terms of the density. Only the first two terms of this series are calculated.
Is it not true that the boundaries of the definite integral in 'x' are the same as 'k' (with periodic BCs) running from -infinity to +infinity (defined at around 4:04)? Otherwise (0 to infinity), I think a (1/2)^3 prefactor will appear in the result (at around 6:36).
