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Thread: help needed integral [1 to 2] (lnx)^2/(x^3)

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

    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 $\displaystyle du= \frac{1}{x} dx$. In this problem that still leaves $\displaystyle x^2$ in the denominator but if u= ln(x), then $\displaystyle x= e^u$ and $\displaystyle \frac{1}{x^2}= e^{-2u}$.

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