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We investigate the existence of Liouville integrable cosmological models inhybrid metric-Palatini theory. Specifically we use the symmetry conditions forthe existence of quadratic in the momentum conservation laws for the fieldequations as constraint conditions for the determination of the unknownfunctional form of the theory. The exact and analytic solutions of theintegrable systems which found in this study are presented in terms ofquadratics and Laurent expansions.

New cosmological solutions in hybrid metric-Palatini gravity from dynamical symmetries