In this paper we prove that the planar self-assembling micelle system
has no Liouvillian, polynomial and Darboux first integrals. Moreover, we show that the system
has only one irreducible Darboux polynomial with the cofactor being if and only if via the weight homogeneous polynomials and only two irreducible exponential factors and with cofactors and respectively with be the unique Darbox invariant of system.