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Math Help - help needed integral [1 to 2] (lnx)^2/(x^3)

  1. #1
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    help needed integral [1 to 2] (lnx)^2/(x^3)

    integral [1 to 2] (lnx)^2/(x^3)

    how would i solve this
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  2. #2
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    Quote Originally Posted by kensington View Post
    integral [1 to 2] (lnx)^2/(x^3)

    how would i solve this
    integration by parts? where u= (ln x)^2 and v=1/x^3

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    \int \frac{(ln(x))^2}{x^3}dx

    When I see a ln(x) and an x in the denominator, the first thing I think of is to substitute u= ln(x). Then du= \frac{1}{x} dx. In this problem that still leaves x^2 in the denominator but if u= ln(x), then x= e^u and \frac{1}{x^2}= e^{-2u}.

    The integral becomes \int ue^{-2u}du which can be done by integration by parts.
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