Suppose $\sigma = (yz + x^2z^2 + 3xy^2z)dx dy dz$ then how do we find a 2 - form $w$ such that $dw = \sigma$?.
As I know that if it would have been $\sigma = \sum_{i} \alpha_{i} dx_{i}$ then as a Pffafian form an integrating factor would exist iff $(X).\nabla \times X = 0$ where $X = (\alpha_{1}, \alpha_{2},....,\alpha_{n})$.
But here $\sigma$ is a 3-form and we have to find a 2 form $w$ such that when exterior derivative $d$ is applied to $w$ then it will result into a 3-form $\sigma$.
Also, any reference which has problems on integrating factors, forms similar to above ones?