Verify the identity using differentiation.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x\sqrt[\phantom{2}]{6x^2+9}dx=\frac{1}{18}(6x^2+9{)}^{\frac{3}{2}}+C$

$\frac{d}{dx}(\frac{1}{18}(6x^2+9{)}^{\frac{3}{2}}+C)=$

Using the indicated $u-$substitution, identify $f$ such that the integral takes the form ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}f(u)du.$

$f(u)=$