Question

Can you help me integrate this function:
ln(e*x) * 1/x. between e and 1.

Answer 1

use the log property first
\(\ln AB = \ln A + \ln B\)

Answer 2

ln e =1

Answer 3

then you need to do a u substitution

Answer 4

1/x + 1/x*ln(x) is that what it is so far?

Answer 5

yeah, but keep it as
\((1+\ln x)/x\)

now do a substitution
u = 1+ln x

du = ... ?

Answer 6

du/dx = 1/x so integral .... du = integral ... 1/x dx

Answer 7

your new integral in terms of "u" will be ??

Answer 8

between 2 and 1?

Answer 9

yes
so we have


got this ?

Answer 10

Yup, thanks, I pretty much understand. So whenever I do a substitution integration, all I end up integrating is u?

Answer 11

not everytime!
in this case

1+ log x was plugged in as 'u'
thats why numerator has u

Answer 12

Ok, and how do I integrate 1+lnx ?

Answer 13

what ?
we did change that to "u" , isn't it ?