# Thread: Integrate:

1. ## Integrate:

how do I integrate this?

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

2. 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!!

3. thanks,

can you show me how you got from

ln(x^2)/2x

to 2ln(x/2x)

4. 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.

5. would the integral be:

(ln(x)^2)/2

6. Originally Posted by PandaNomium
would the integral be:

(ln(x)^2)/2
Does it give the correct derivative?

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