hello i was asked to from a list a multiple choice which answer when inegrated gives the result $\displaystyle x - lnx^2$

to get that answer i differentiated the function to get the answer which was $\displaystyle x-2/x$

i am now trying to integrated that but cannot get back my answer.

can someone show me how this is done..

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

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

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

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