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Math Help - Change of variables problem

  1. #1
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    Change of variables problem

    I'm currently stuck on the following problem: Using a change of variables but without evaulating the integral, show that:
    \int_{1}^{\infty}\frac{lnx}{x^2 } dx = - \int_{0}^{1}lnx  dx
    I've tried all sorts of substituions (lnx, lnx/x, lnx/x^2, 1/x^2) but nothing seems to give the desired result. Could somebody please give me a hint?

    Many Thanks
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    substitution x=\dfrac1t will solve the problem.
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  3. #3
    Senior Member
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    [duplicate post]

    Try \frac{1}{x}.
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