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Math Help - Integrate:

  1. #1
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    Integrate:

    how do I integrate this?

    int: {[ln (x^2)]/2x} dx
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by PandaNomium View Post
    how do I integrate this?

    int: {[ln (x^2)]/2x} dx

    Note that the integrand is

    \frac{\ln (x^2)}{2x} = ( 2 \ln x ) \left( \frac{1}{2x} \right) = \left( \frac{1}{x} \right) \ln x

    Also note that the first derivative of the natural log of x is \frac{1}{x}


    Good luck!!
    Last edited by mr fantastic; September 22nd 2009 at 08:24 PM. Reason: Added brackets to make the reply more obvious
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  3. #3
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    thanks,

    can you show me how you got from

    ln(x^2)/2x

    to 2ln(x/2x)
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  4. #4
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    Quote Originally Posted by PandaNomium View Post
    thanks,

    can you show me how you got from

    ln(x^2)/2x

    to 2ln(x/2x)
    I edited the earlier reply by adding brackets. Read it again. The answer to your question should now be clearer.

    Note also: \ln x^2 = 2 \ln |x| not 2 \ln x. The modulus is important.
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  5. #5
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    would the integral be:

    (ln(x)^2)/2
    Last edited by PandaNomium; September 23rd 2009 at 05:45 AM.
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  6. #6
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    Quote Originally Posted by PandaNomium View Post
    would the integral be:

    (ln(x)^2)/2
    Does it give the correct derivative?
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  7. #7
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    To check if your integral is correct take the derivative of it and you should get your original integrand back
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