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Math Help - integrating

  1. #1
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    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
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  2. #2
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     \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
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