Integration by parts and simplifying

[trajan22]

Hi,
I have been working on this problem for the longest time and have just run in circles with it. I am thinking the answer is obvious but for some reason I am 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.

 

[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.

 

[trajan22]

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

 

[stunner5000pt]

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

thts correct

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

 

[trajan22]

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

 

[acm]

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