Is $\omega = x^2\,dy\,dz +y^2\,dz\,dx + z^2\,dx\,dy$ exact?

Question

this isn't a homework problem or anything. Basically is $\omega = x^2 \,dy\,dz +y^2\,dz\,dx + z^2\,dx\,dy$ exact? That is, is there a $\lambda$ such that $\omega=d\lambda$, if so what is it?

I think it is not exact but not entirely sure how to show that.

Answer 1

$d\omega=2x\,dx\,dy\,dz+2y\,dy\,dz\,dx+2z\,dz\,dx\,dy=2(x+y+z)\,dx\,dy\,dz\neq0$

Hence $\omega$ is not closed, therefore not exact.