Question

integration of dx/xlnx

Answer 1

try to put u = ln x
then du= ... ?

Answer 2

i split it to \[\frac{ 1 }{ x } . \frac{ dx }{ lnx }\] and thenlet u= lnx and du=1/x
then it would be \[\int\limits_{}^{}du.\frac{ 1 }{ u}\]
which = ln(u) which =ln(ln(x)) am i correct?

Answer 3

absolutely correct! :)
just don't forget the +c
ln (ln x) +c
:)

Answer 4

thanks hartnn!

Answer 5

welcome ^_^

Answer 6

you can also verify it by differentiating the function
d/dx (ln (ln x)) = (1/ln x) d/dx (ln x) = 1/ (x ln x)