Evaluate the following integral or state that it diverges.

${\displaystyle \underset{-}{\overset{}{}}}6x{e}^{-3x^2}dx$

Select the correct choice and, if necessary, fill in the answer box to complete your choice.

A$.$ The integral converges and ${\displaystyle \underset{-}{\overset{}{}}}6x{e}^{-3x^2}dx=($Type an exact answer.$)$

B$.$ The integral diverges.