Evaluate the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{u}(u^3-1)du.$

Select one:

$a.\frac{2}{9}{u}^{\frac{9}{2}}+u^{\frac{3}{2}}+C$

$b.\frac{2}{9}{u}^{\frac{9}{2}}-\frac{2}{3}{u}^{\frac{3}{2}}+C$

$c.\frac{(\sqrt[\phantom{2}]{u}{)}^2}{2}\frac{(u^3-1{)}^2}{2}+C$

$d.3\frac{u^{\frac{3}{2}}}{2}\frac{(u^3-1{)}^2}{2}+C$