How do I find this integral?

Question

1/(x ln x)*dx

Answer 1

I = ∫ 1 / [ x ln x ] dx
Let u = ln x
du = (1/x) dx
I = ∫ 1 / u du
I = ln u + C
I = ln (ln x) + C

Answer 2

Take t=ln x

then dt/dx = 1/x

integral 1/(x ln x) dx = integral (1/t) (1/x) dx =
= integral (1/t) dt = ln|t| + c = ln |ln |x|| + c

Answer 3

let lnx =t
differentiate
1/x dx =dt

substitute this in the question

1/t dt

integtrate now we get

lnt

substitute the value of t we get
ln(lnx) +c