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Math Help - Help me with integration by parts

  1. #1
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    Help me with integration by parts



    Please evaluate by using integration by parts.
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  2. #2
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    Hi there, yang03265...

    Using parts we can first of all integrate log of x...





    Straight lines integrate up or differentiate down, so that the triangular network satisfies the product rule for differentiation. The
    challenge of integration by parts is simply to fill out this product shape usefully but starting (unlike when differentiating) with one of the lower
    balloons.

    We can use the above result to do your integral...





    Now solve the top row for \int x \ln^2 x

    Don't integrate - balloontegrate!

    Balloon Calculus: worked examples from past papers
    Last edited by tom@ballooncalculus; February 17th 2009 at 05:28 AM. Reason: typo
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  3. #3
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    Pardon me - this way much simpler, of course...





    Thanks, red dog
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