$\displaystyle \int 2(x+1)dx$
Method 1
$\displaystyle u=x+1$
$\displaystyle du=dx$
$\displaystyle \int 2udu$
$\displaystyle u^2+c$
$\displaystyle (x+1)^2+c$
Method 2
$\displaystyle \int (2x+2) dx$
$\displaystyle x^2+2x+c$
???
$\displaystyle \int 2(x+1)dx$
Method 1
$\displaystyle u=x+1$
$\displaystyle du=dx$
$\displaystyle \int 2udu$
$\displaystyle u^2+c$
$\displaystyle (x+1)^2+c$
Method 2
$\displaystyle \int (2x+2) dx$
$\displaystyle x^2+2x+c$
???