9.9.3 Potential and solenoidal fields

Problem: Show that the field \( \vec{a} \) is potential and find its potential: \[ \vec{a}=\left(\frac{y}{z}+z\right) \vec{\imath}+\left(\frac{x}{z}-\frac{1}{y^{2}}\right) \vec{\jmath}+\left(x-\frac{x y}{z^{2}}\right) \vec{k} . \]