We now use the substitution $u=4x^{2}6$ and $du=8xdx$ to convert the entire integral into one involving only $u.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}8x(4x^{2}6{)}^{6}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(4x^{2}6{)}^6(8xdx)$

$={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}()du$