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

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^6+x^5+x^2{)}^7(6x^5+5x^4+2x)dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^6+x^5+x^2{)}^7(6x^5+5x^4+2x)dx=$

$($Type an exact answer. Use parentheses to clearly denote the a