how do I integrate this? int: {[ln (x^2)]/2x} dx
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Originally Posted by PandaNomium how do I integrate this? int: {[ln (x^2)]/2x} dx Note that the integrand is $\displaystyle \frac{\ln (x^2)}{2x} = ( 2 \ln x ) \left( \frac{1}{2x} \right) = \left( \frac{1}{x} \right) \ln x$ Also note that the first derivative of the natural log of x is $\displaystyle \frac{1}{x}$ Good luck!!
Last edited by mr fantastic; Sep 22nd 2009 at 08:24 PM. Reason: Added brackets to make the reply more obvious
thanks, can you show me how you got from ln(x^2)/2x to 2ln(x/2x)
Originally Posted by PandaNomium 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: $\displaystyle \ln x^2 = 2 \ln |x|$ not $\displaystyle 2 \ln x$. The modulus is important.
would the integral be: (ln(x)^2)/2
Last edited by PandaNomium; Sep 23rd 2009 at 05:45 AM.
Originally Posted by PandaNomium would the integral be: (ln(x)^2)/2 Does it give the correct derivative?
To check if your integral is correct take the derivative of it and you should get your original integrand back
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