Math Help - integrating

1. integrating

hello i was asked to from a list a multiple choice which answer when inegrated gives the result $x - lnx^2$
to get that answer i differentiated the function to get the answer which was $x-2/x$

i am now trying to integrated that but cannot get back my answer.
can someone show me how this is done..

$let u =x-2$ and d $v = x^-1$

therefore $du/dx = -2$ and $v = lnx$

using the formula i have $(x-2)(lnx) -\int (x)^-1 (-2)$

can some one please show me where am going wrong. note m

2. $\frac{d}{dx}(x-\ln(x^2))= 1-\frac{2}{x}$

$\int 1-\frac{2}{x}~dx = x-2\ln(x) +C= x-\ln(x^2)+C$