Find the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x\sqrt[\phantom{2}]{x-1}dx$ using substitution. The resulting integral is $.....$

A$.x*\frac{2}{3}(x-1{)}^{\frac{3}{2}}C$

B$.\frac{1}{2}{x}^2*\frac{2}{3}(x-1{)}^{\frac{3}{2}}C$

C$.\frac{2}{5}(x-1{)}^{\frac{5}{2}}\frac{2}{3}(x-1{)}^{\frac{3}{2}}C$

D$.$ None of these

E$.\frac{2}{5}(x1{)}^{\frac{5}{2}}\frac{2}{3}(x1{)}^{\frac{3}{2}}C$