  We derive the ground-state energy of $N$ composite bosons made of fermion
pairs using the recently developed composite boson many-body formalism. We
concentrate on the $N$-pair energy linear in density. We show that the
scattering relevant for scattering length contains not only direct and exchange
interaction scatterings but also the dimensionless "Pauli scattering" for
fermion exchange in the absence of fermion-fermion interaction. Numerical
resolution of the resulting "ladder" integral equation for fermions interacting
through long-range Coulomb forces --- which act as effective repulsion between
excitons made of same-spin electrons and same-spin holes --- shows that the
prefactor of the $N$-exciton energy linear in density is substantially
decreased from its Born approximation value, $13\pi/3$, by a factor
$\simeq0.38$ for equal electron and hole effective masses. Interestingly, this
factor goes to zero when the hole mass goes to infinity, making the
triplet-exciton gas unstable in this limit.
