Answer
$\int 2(2x+4)^{4}dx = \frac{(2x+4)^5}{5}$
Work Step by Step
$\int 2(2x+4)^{4}dx \space\space\space\space\space u = 2x+4$
First, we organize the integral
$\int (2x+4)^4 2dx$
Now, we find $du$
$\frac{du}{dx}=2(x^{1-1}) + 0$
$du = 2dx$
And we do the substituition
$\int (u)^4 du$
To finish, we find the antiderivative of this integral applying the power rule for integrals
$\int(u)^4 du = \frac{u^{4+1}}{4+1}$
$\int(u)^4 du = \frac{u^5}{5}$
And now we go back to $x$
$\int 2(2x+4)^{4}dx = \frac{(2x+4)^5}{5}$
