Invariant integrability conditions for ternary differential systems with quadratic nonlinearities of the Darboux form

The general integral for ternary differential system with quadratic nonlinearities of the Darboux form was constructed by using the Lie theorem on integrating factor. The case is achieved when the comitant of the linear part of differential system, which is a $GL(3,\mathbb R)$-invariant particular integral, describes an invariant variety.