The integration of experimental data and simulations is a powerful approach to increase the resolution of the former and the accuracy of the latter . This integration is based on two elements, (i) a forward model for the calculation of an experimental observable given a conformation and (ii) an integration strategy (e.g., restraints or reweighting based on either the maximum entropy principle or Bayesian inference ). The forward model should be accurate and computationally efficient when the goal is to apply a restraint in a simulation. In this work we have presented an implementation of a SAXS and SANS forward model that efficiently exploits the limited resolution of these experimental techniques. In particular, it allows protein and nucleic acid scattering to be represent by a single-bead per amino acid and a three-bead per nucleic acid residue, and more importantly, it enables the effective on-the-fly inclusion of solute-solvent scattering corrections at no cost. We showed that the inclusion of this correction modifies the resulting conformations by mildly decreasing their radius of gyration as expected and matching WAXSiS, a more accurate but expensive forward model. The method presented here is already deployed in PLUMED thus allowing its use in combination with different molecular dynamics engines, restraining strategies including metainference and maximum entropy /caliber 86 approaches, or enhanced sampling techniques such as metadynamics and umbrella sampling .