  We consider the Lieb-Liniger model for a gas of bosonic $\delta-$interacting
particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic
limit of the form factors of the density operator between finite entropy
eigenstates such as finite temperature states or generic non-equilibrium highly
excited states. These form factors are crucial building blocks to obtain the
thermodynamic exact dynamic correlation functions of such physically relevant
states. As a proof of principle we compute an approximated dynamic structure
factor by including only the simplest types of particle-hole excitations and
show the agreement with known results.
