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

I

imattxc

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

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...
 
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imattxc said:
So the problem is \(\displaystyle \displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}\)
Click to expand...

What is the derivative of \(\displaystyle \log((\log(x)))~?\)
 
Last edited by a moderator:
imattxc said:
So the problem is \(\displaystyle \displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}\)

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...
Click to expand...
substitute:

u = log(x)
 
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