i.i.6 Potential and solenoidal fields

condition: Prove that the field \[ \bar{F}=\left(\frac{1}{1+x^{2}}+e^{2 y} \cos 2 x\right) i+\left(\frac{1}{y}+e^{2 y} \sin 2 x\right) j \] is potential. Find the potential and calculate the work done by this field on the path from \( A(1,2)\) to \( B(3,4)\).