# Integrating indefinitely: (ln x)/x^3

1. Jun 8, 2008

### roq2

edit: Nevermind, I realized a way to find the answer after posting it. Though I still don't know about the thing involving the notes, can someone confirm if what I have written down as my teacher doing is true?

1. The problem statement, all variables and given/known data
note: I'll use this S as an integral symbol.

S(ln x)/x^3

2. Relevant equations

3. The attempt at a solution
With a ln x type function being divided by a power of x, I did the obvious and made u = ln x and du = 1/x dx, but that still leaves x^-2. I don't know how to get from here.

I just saw this problem in my notes and am not sure if I made an error when writing, but what my teacher appears to have done is made the same substitution I did, and then wrote
S(ln x)/x^3 = Se^(-2u) du.

I don't know how one makes that, and when I plug back the substitution I don't arrive at the original equation. I get e^(-2 ln x)*dx/x = (x^2)/x * dx (I split e^-2 ln x into (e^-ln x)(e^-ln x) = -x^2. So I think I just wrote something down wrong, but in any case, I still do not know how to go beyond that simple substitution I made earlier.

edit: I just needed to integrate by parts with ln x = u and dv = 1/x^3

Last edited: Jun 8, 2008
2. Jun 8, 2008

### rock.freak667

Yes integration by parts would work,but the substitution of u=lnx works as well,though longer

$du=\frac{dx}{x}$

and $u=lnx \Rightarrow x=e^u$

so you can find $x^{-2}$ from that and you'll get what he did.

3. Jun 8, 2008

### roq2

Thank you. :p