Answer
$\dfrac{(x+2)^8}{8}-\dfrac{2(x+2)^7}{7}+C$
Work Step by Step
We will solve the given integral by using u-substitution method.
Suppose that $x+2=u \implies dx=du$
$\displaystyle \int x (x+2)^6 \ dx=\int (u-2) u^6 \ du $
or, $=\dfrac{u^8}{8}-\dfrac{2u^7}{7}+C$
Now, back subtiture $u=x+2$
Therefore, we have: $\displaystyle \int x (x+2)^6 \ dx=\dfrac{(x+2)^8}{8}-\dfrac{2(x+2)^7}{7}+C$
