Differential

\hspace{-16}$\sqrt{1+x^2+y^2+x^2.y^2}=\displaystyle xy\frac{dy}{dx}$\\\\ $\sqrt{\left(1+x^2\right).\left(1+y^2\right)}=xy\displaystyle \frac{dy}{dx}$\\\\ $\sqrt{1+x^2}.\sqrt{1+y^2}=xy\displaystyle \frac{dy}{dx}$\\\\ $\displaystyle \frac{\sqrt{1+x^2}}{x}.dx=\frac{y.dy}{\sqrt{1+y^2}}$\\\\ $Now Integrate both side\\\\ $\displaystyle \int \frac{\sqrt{1+x^2}}{x}.dx=\int \frac{y.dy}{\sqrt{1+y^2}}$\\\\