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Math Help - Please help with integration

  1. #1
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    Please help with integration

    Hi there,

    I am not too sure how to go about the question 'integrate xlnx dx'
    the answer is meant to be (x^2lnx)/2-x^2/4+C

    could someone help please?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Please help with integration

    Use integration by parts. Let:

    u=\ln(x)\,\therefore\.du=\frac{1}{x}\,dx

    dv=x\,dx\,\therefore\,v=\frac{x^2}{2}

    and then:

    \int x\ln(x)\,dx=uv-\int v\,du
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  3. #3
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    Re: Please help with integration

    Oh, ok!! I think I had messed up the 'u', 'du', 'dv' and 'dv' before.

    Thank you so much for your help
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  4. #4
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    Re: Please help with integration

    when integrating -x^2(1/x dx), why does 2 become a numerator (e.g. (2-x^2)/4)
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Please help with integration

    I'm not sure what you are asking, but:

    -\int v\,du=-\int \frac{x^2}{2}\cdot\frac{1}{x}\,dx=-\frac{1}{2}\int x\,dx=-\frac{x^2}{4}+C
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  6. #6
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    Re: Please help with integration

    Usually integration by parts with lnx and some polynomial term in x, you use lnx term to be u, so that, differentiating it cancels other term (more of an exam tip).

    Salahuddin
    Maths online
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: Please help with integration

    I use the LIATE mnemonic to determine which should be u.
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