indefinite integral of 1 / (x ln(x))

[flyguy03]

i need help finding the indefinite integral of { 1/ (x lnx) dx

i let u = lnx and then I found

{ 1/u du the answer i got is

1/ (ln (lnx)) + C

I am not sure that it is right as this is not the answer in the back of the book.

Thanks

 

[galactus]

You strayed a wee bit at the end.

Let \(\displaystyle u=ln(x)\) and \(\displaystyle du=\frac{1}{x}dx\)

You then get:

\(\displaystyle \L\\\int\frac{1}{u}du\)

When you integrate you get \(\displaystyle ln(u)\)

Resub u:

\(\displaystyle ln(ln(x))+C\)

You just had the reciprocal of this.