Find the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^5\sqrt[\phantom{2}]{3+u^6}du.$

$\frac{2(3+u^6{)}^{\frac{3}{2}}}{18}+C$

$\frac{2(3+u^6{)}^{\frac{2}{3}}}{18}+C$

$\frac{(3+u^6{)}^{\frac{3}{2}}}{12}+C$

$\frac{2(3+u^6{)}^{\frac{5}{2}}}{30}+C$

$\frac{(3+u^6{)}^{\frac{3}{2}}}{18}+C$