# Thread: Improper Integral of 1/(xln(x)) from e to infinity help?

1. ## Improper Integral of 1/(xln(x)) from e to infinity help?

So the problem is $\displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}$

I know I would need to get the limit from n to infinity and swap infinity in the integral with n.
I don't know what to do with (1/(xlnx))dx . I cant do by sums and wen I do by parts I cant find dv which I set to ln(x)^(-1)dx. Im just not sure where to go with this...

2. Originally Posted by imattxc
So the problem is $\displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}$
What is the derivative of $\log((\log(x)))~?$

3. Originally Posted by imattxc
So the problem is $\displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}$

I know I would need to get the limit from n to infinity and swap infinity in the integral with n.
I don't know what to do with (1/(xlnx))dx . I cant do by sums and wen I do by parts I cant find dv which I set to ln(x)^(-1)dx. Im just not sure where to go with this...
substitute:

u = log(x)