Evaluate ${\displaystyle \underset{2}{\overset{3}{}}}x\sqrt[\phantom{2}]{x-1}dx$

$2$

$2\sqrt[\phantom{2}]{8}-\frac{4}{15}\sqrt[\phantom{2}]{32}-\frac{16}{15}$

$\frac{16}{15}$

$\sqrt[\phantom{2}]{2}+\frac{3}{2\sqrt[\phantom{2}]{2}}-2$