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

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(6t^5+7)t^{4}dt$

Determine a change of variables from $t$ to $u.$ Choose the correct answer below.

A$.u=t^4$

B$.u=6t^5+7$

C$.u=6t+7$

D$.u=t^4+7$

Write the integral in terms of $u.$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(6t^5+7)t^{4}dt={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}du$

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

Evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(6t^5+7)t^{4}dt=$

$$

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