The development of industrial bioprocesses requires reliable mathematical models that describe microbial growth, substrate consumption, and product formation. These models must provide precise simulations of bioprocesses to aid in the development of design equations for biological reactors. This work introduces integral forms of the Pirt and Luedeking-Piret models. With the specific biomass growth rate estimated by any model, these expressions can be used to simulate substrate uptake and product formation. They were validated using the Gompertz model as a particular case study. The analytical solutions obtained were used for simulating lactate uptake and acetate formation during Megasphaera elsdenii culturing. The experimental data on biomass growth were accurately fitted to the Gompertz model ( R adj 2 = 0.985). Similarly, coupled models were used to simulate lactate uptake and acetate formation, with a high goodness of fit ( R adj 2 > 0.969). Therefore, the models accurately simulate the lactate and acetate concentrations and their respective instantaneous and specific rates. Additionally, the analysis revealed that biomass growth is proportional to lactate-to-acetate conversion, indicating that most of the energy from substrate consumption is directed to biomass growth. The developed models are helpful tools for obtaining accurate information for designing, optimizing, and scaling various