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Math Help - Integral Calculus.

  1. #1
    Newbie summer072693's Avatar
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    Integral Calculus.

    Hi there mathematicians.. I just wanna ask some help for solving this problem. I got stuck when answering this..
    what would be the best approach for solving this?
    integrate lnx ln(1-x) dx, from 0 to 1.
    Last edited by summer072693; November 15th 2012 at 05:20 AM.
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  2. #2
    MHF Contributor
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    Re: Integral Calculus.

    Here's one way...



    Spoiler:




    ... gets a bit hairy, but I think you can evaluate using Polylogarithm -- from Wolfram MathWorld



    ... where (key in spoiler) ...

    Spoiler:




    ... is the product rule, where, straight continuous lines are differentiating downwards with respect to x. (I've used the triple version of the rule as well - see wikipedia.)



    ... is lazy integration by parts, doing without u and v.




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    Last edited by tom@ballooncalculus; November 15th 2012 at 06:58 AM.
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