Question

How do I integrate this? (see first post for the integral)

Answer 1

\[\int\limits_{}^{}\frac{ \ln x }{ x^2 }dx\]

Answer 2

I think I can use substitution, but I'm not sure how...

Answer 3

Well, you CAN use substitution... you usually pick the logs anyway...
let u = ln(x)
:)

Answer 4

ok.
so if

u = ln x
\[du = \frac{ 1 }{ x }dx\]

and the integral is now
\[\int\limits_{}^{}\frac{ u }{ x}du\]
because I can only pull out one of the x's in the denominator

how to I get rid of the other x? is it easier to solve this integral a different way?

Answer 5

Of course, you do this by parts :)
But remember...
\[\huge u=\ln(x) \rightarrow x=e^u\]
AND
\[\huge \frac{1}x=x^{-1}=(e^u)^{-1}=e^{-u}\]
And that about sums it up, don't you think?

^.^

Answer 6

you could do one derivative by parts. then do a regular integration