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Math Help - [SOLVED] Integral

  1. #1
    MHF Contributor arbolis's Avatar
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    [SOLVED] Integral

    How would you solve \int \ln (\sqrt{x^2+x+1}) dx?
    I don't see any good substitution nor a good integration by part. I'm not asking the whole solution, just the way you'd solve it.
    Thanks.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Note that \log((x^2+x+1)^{1/2}) = \frac{1}{2}\log\Big(\frac{x^3-1}{x-1}\Big)

    =\frac{1}{2}\Big(\log(x^3-1)-\log(x-1)\Big)
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  3. #3
    Senior Member pankaj's Avatar
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    \frac{1}{2}\int1.\ln(x^2+x+1)dx=\frac{x}{2}\ln(x^2  +x+1)+...............
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