i.i.7 Potential and solenoidal fields

condition: Prove the potentiality of a given vector field and find its potential using a curvilinear integral. \[ \begin{array}{l} \vec{a}=(2 x y z+7) \vec{\imath}+\left(x^{2} z-12 y^{2} z\right) \vec{\jmath}+ \\ +\left(x^{2} y-4 y^{3}+4 z^{3}\right) \vec{k} \end{array}\]