Darboux first integral conditions and integrability of the 3D   Lotka-Volterra system
  We apply the Darboux theory of integrability to polynomial ODE's of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3-dimensional Lotka-Volterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases of integrability. 
Laurent Cair\'o