integrating

Apr 2010
135
0
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
Sep 2008
5,237
1,625
Melbourne
\(\displaystyle \frac{d}{dx}(x-\ln(x^2))= 1-\frac{2}{x}\)

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