Integrate:

**PandaNomium** · September 22nd 2009, 05:10 PM

how do I integrate this?

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

**apcalculus** · September 22nd 2009, 05:21 PM

Originally Posted by PandaNomium

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!!

**PandaNomium** · September 22nd 2009, 05:31 PM

thanks,

can you show me how you got from

ln(x^2)/2x

to 2ln(x/2x)

**mr fantastic** · September 22nd 2009, 08:26 PM

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: $\ln x^2 = 2 \ln |x|$ not $2 \ln x$ . The modulus is important.

**PandaNomium** · September 23rd 2009, 05:35 AM

would the integral be:

(ln(x)^2)/2

**mr fantastic** · September 23rd 2009, 03:02 PM

Originally Posted by PandaNomium

would the integral be:

(ln(x)^2)/2

Does it give the correct derivative?

**mmattson07** · September 23rd 2009, 03:31 PM

To check if your integral is correct take the derivative of it and you should get your original integrand back

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