Evaluate. $($Be sure to check by differentiating!$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(4+x^7{)}^{6}7x^{6}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(4+x^7{)}^{6}7x^{6}dx=$

$($Type an exact answer. Use parentheses to clearly denote the argument of each function.$)$