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Math Help - Integration

  1. #1
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    Integration

    Hi. I'm trying to integrate \int\frac{1+lnx}{xlnx}\ dx I think it's of the form f'(x)/f(x) so shouldn't the answer be ln(xlnx)? This is not the answer in the back of the book however.
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  2. #2
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    Split it up into two integrals.
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  3. #3
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    so i get \int\frac{1}{x} + \int\frac{1}{lnx} but then how do I integrate 1/lnx dx? if I use substitution the dx gets messy.
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  4. #4
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    Quote Originally Posted by flashylightsmeow View Post
    so i get \int\frac{1}{x} + \int\frac{1}{lnx} but then how do I integrate 1/lnx dx? if I use substitution the dx gets messy.
    Surely, \displaystyle \frac{1+\ln{x}}{x\ln{x}} \ne \frac{1}{x}+\frac{1}{\ln{x}}?
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  5. #5
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    sorry, 1/x + 1/xlnx, is that correct?
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  6. #6
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    Quote Originally Posted by flashylightsmeow View Post
    sorry, 1/x + 1/xlnx, is that correct?
    Yes, note that \displaystyle \frac{1}{x\ln{x}} = \frac{1/x}{\ln{x}}.
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  7. #7
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    Yes, \dfrac{1 + \ln x}{x\ln x} = \dfrac{1}{x} + \dfrac{1}{x\ln x}.

    Edit: I was a little slow. :P
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  8. #8
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    Quote Originally Posted by NOX Andrew View Post
    Edit: I was a little slow. :P
    Same minute! Talk about luck on my part!
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  9. #9
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    Thanks guys.
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