# Integration by parts and simplifying

1. Jan 5, 2007

### trajan22

Hi,
I have been working on this problem for the longest time and have just run in circles with it. Im thinking the answer is obvious but for some reason Im missing it. I need to find $$\int \frac{ln(x)}{x^2} dx$$ I know that I need to use integration by parts and have tried a number of things, however the only way that the integral seems to be simplified is if I use this set up
u=ln(x) du=1/x
v=? dv=1/(x^2)
but from here I cannot integrate 1/x^2. Am i even on the right track with this one or is there an easier way? someone please help as this problem is truly annoying me.

2. Jan 5, 2007

### ChaoticLlama

you're on the right track, but try thinking of 1/x^2 as polynomial, ie: x^(-2).
I'm sure you can integrate that.

3. Jan 5, 2007

### trajan22

oh yeah thats right...ok so if i integrate that then its simply -(1/x) correct?

4. Jan 6, 2007

### stunner5000pt

thts correct

(if you are unsure try differentiating (-1/x))

5. Jan 6, 2007

### trajan22

oh yeah thats right...I always forget that its really easy to check these types of problems...thanks for all the help

6. Jan 6, 2007

### acm

I : lnx/x^2 dx
I: (-lnx/x) - I(1/x^2) dx
I: -lnx/x + 1/x + K