  In this paper it is shown that the existence of two independent holomorphic
first integrals for foliations by curves on (C^3,0) is not a topological
invariant. More precisely, we provide an example of two topologically
equivalent foliations such that only one of them admits two independent
holomorphic first integrals. The existence of invariant surfaces over which the
induced foliation possesses infinitely many separatrices possibly constitutes
the sole obstruction for the topological invariance of complete integrability
and a characterization of foliations admitting this type of invariant surfaces
is also given.
