  We consider the problem of computing dynamic correlation functions of quantum
integrable models employing the thermodynamic form-factor approach.
Specifically, we focus on correlations of local operators that conserve the
number of particles and consider the 2-particle-hole contribution to their
two-point functions. With the method developed being generally applicable to
any finite energy and entropy state, our primary focus is on the thermal
states. To exemplify this approach, we chose the Lieb-Liniger model and study
the leading contribution from 2-particle-hole excitations at small momenta to
the dynamic density-density correlation function. We also consider analogous
contributions to two-point functions of higher local conserved densities and
currents present in integrable theories.
