Show that the differential equation: 

is integrable and find its integral.

To show that the given differential equation is integrable, we can check if it satisfies the condition of being exact. A differential equation of the form \(Mdx + Ndy + Pdz = 0\) is exact if and only if \(\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}\), \(\frac{\partial M}{\partial z} = \frac{\partial P}{\partial x}\), and \(\frac{\partial N}{\partial z} = \frac{\partial P}{\partial y}\).

Given the equation:
\[ (y^2 + yx)dx + (z^2 + zx)dy + (xy)dz = 0 \]

Let's calculate the partial derivatives:

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