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Math Help - integral help

  1. #1
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    integral help

    Evalute the integral:

    ((1-x)/x)^2 dx

    I think I need to do integration by parts by I don't know the steps... please help

    Thanks.
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Evalute the integral:

    ((1-x)/x)^2 dx

    I think I need to do integration by parts by I don't know the steps... please help

    Thanks.
    No need for integration by parts.

    Recall that \frac{1 - x}{x} = \frac{1}{x} - 1 = x^{-1} - 1.

    So \left(\frac{1 - x}{x}\right)^2 = (x^{-1} - 1)^2

     = x^{-2} - 2x^{-1} + 1.


    Therefore

    \int{\left(\frac{1 - x}{x}\right)^2\,dx} = \int{x^{-2} - 2x^{-1} + 1\,dx}

     = -x^{-1} - 2\ln{|x|} + x + C

     = x - \frac{1}{x} - 2\ln{x} + C.
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  3. #3
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     <br />
\int \left(\frac{1-x}{x}\right)^2~dx = \int \left(\frac{1}{x}-1\right)^2~dx= \int \left(\frac{1}{x^2}-\frac{2}{x}+1\right)~dx<br />

    now integrate it term by term.
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