Question

Integrate 1/lnx from e to inf

Answer 1

it diverges to infinity

Answer 2

Please write out

Answer 3

I don't have time...I have to teach...try comparing 1/ln(x) to 1/x

Answer 4

What Z's arguing is this.

For x > 1\[0 < \ln x < x \ \implies 1/x < 1/\ln x\]

Now consider the integral of 1/x from e to infinity does that integral exist? If it diverges to +infinity, then the integral over the same range of 1/ln x must as well.