Question

integrates 1/x(logx)powerof n w.r.t.x

Answer 1

u=ln(x)

Answer 2

\[\int\limits \frac{1}{ x [\ln(x)]^n} dx\]

Answer 3

if its that^

Answer 4

if its that^

Answer 5

let

u=ln(x)
du = (1/x) dx

Answer 6

\[= \int\limits \frac{1}{u^n} du \]

Answer 7

\[= \int\limits u^{-n} du = \frac{u^{-n+1} }{1-n} +C \]

Answer 8

but that is only for \[n \neq \]

Answer 9

\[= \frac{ (\ln(x))^{1-n} }{ 1-n} +C \]

for \[n \neq 1\]

= \[\ln(\ln(x)) +C \] for n=1