\[{\text{Let }}a,b,c \in \mathbb{R},{\text{ }}0 < a < b.{\text{ Show that}}\] $$\int\limits_0^1 {{{\left( {{x^a} - {x^b}} \right)}^c}dx} = \frac{{\Gamma \left( {\frac{{ac + 1}}{{b - a}}} \right) \cdot \Gamma \left( {c + 1} \right)}}{{\Gamma \left( {\frac{{bc + 1}}{{b - a}}} \right) \cdot \left( {bc + 1} \right)}}.$$