We study the integrability of two-dimensional autonomous systems in the plane of the formẋ = −y + X s (x, y),ẏ = x + Y s (x, y), where X s (x, y) and Y s (x, y) are homogeneous polynomials of degree s with s ≥ 2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable (x 2 + y 2 ) s/2−1 with coefficients being functions of tan −1 (y/x).