Descent methods for studying integer points on $y^n=f(x)g(x),n\ge 2$

We study the integer points on superelliptic and hyperelliptic curves of the form $y^n=f(x)g(x),$ $n\ge 2,\mathrm{d}\mathrm{e}\mathrm{g}f+\mathrm{d}\mathrm{e}\mathrm{g}g\ge 4.$