# integrating

#### sigma1

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

#### pickslides

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

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