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Math Help - Integral of ln Squared?

  1. #1
    Member iPod's Avatar
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    Integral of ln Squared?

    \int\ln^2(x)dx

    Hints please?
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  2. #2
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    Looks like a prime candidate for "Parts". It's almost an eyeball problem.

    x\cdot ln^{2}(x) - \int x\cdot 2\cdot ln(x)\cdot \frac{1}{x}\;dx
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  3. #3
    Member iPod's Avatar
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    soo,

    \ln^2(x)-2x\ln(x)+2x+C

    ??
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  4. #4
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    close, try  x\ln^2(x)-2x\ln(x)+2x+C
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  5. #5
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    So close! Give it another go. This time, don't lose the 'x' on the front.
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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by iPod View Post
    soo,

    \ln^2(x)-2x\ln(x)+2x+C

    ??
    You should get
    x\ln^2(x)-2x\ln(x)+2x+C
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  7. #7
    Member iPod's Avatar
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    woopsy, that was a typo ^^

    i meant to right
    x\ln^2(x)-2x\ln(x)+2x+C

    but I have seen what you have done tkhunny, using the 'by parts rule, you have integrated it as if it was

    \int1.\ln^2(x)

    right?
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  8. #8
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    Quote Originally Posted by iPod View Post

    \int1.\ln^2(x)

    right?
    Yep with v = \ln^2x and du = 1
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  9. #9
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    Thanks you lot
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  10. #10
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    ...except that I don't use that silly American method. The Russians are much more visual and literal.
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