Question

finding integral involving ln (x) / x?

Answer 1

did u try "u sub" ?

Answer 2

So I had a problem
\[\int\limits_{1}^{e}\frac{ \ln(x) }{ x }dx\]
I thought it would just be a simple u-substitution, so I ended up solving
u = lnx
du = 1/x dx
and ended up with
\[\left[ \frac{ (lnx)^2 }{ 2 } \right]\]
from 0 to 1
but the probme is!

Answer 3

I ended up with [ln 0]^2 and that can't BE SOLVED!

Answer 4

help. :p

Answer 5

bounds will not change since u switched back to x's

Answer 6

you just need to evaluate that from 1 to e

Answer 7

\(\large \left[ \frac{ (\ln x)^2 }{ 2 } \right]_1^e \)

Answer 8

Oh, but if I solve it with u, would it be the same? Right... I was missing that, thanks for pointing it out.

Answer 9

\(\large \left[ \frac{ (\ln x)^2 }{ 2 } \right]_1^e \)


or


\(\large \left[ \frac{ u^2 }{ 2 } \right]_0^1 \)

Answer 10

both are okay

Answer 11

They both lead to the same answer, thanks ganeshie.

Answer 12

you're wlcme :)