Integral from 1 to infinity of 1 / xln(third root of x)

[poopforfood]

Homework Statement

Integral from 1 to infinity of 1 / xln(third root of x)

2. Homework Equations

n/a

3. The Attempt at a Solution

I tried to find if it diverged and then got lost after that

Homework Equations

The Attempt at a Solution

 

[bob1182006]

if it diverges then that's the final answer. But can you post your work? maybe you did a mistake. But I think it is supposed to diverge.

 

[poopforfood]

well you see there bob I am not too sure how to get started and what to do with the ln

 

[Dick]

If you don't know what to do, then you don't know it diverges, right? Try a substitution u=ln(x).

 

[danni7070]

Dick: I did u = ln(x) and du = 1/x

so int from 1 to 0 ln(third root of u)du

= - in from 0 to 1 ln(third root of u)du

I always mix up these substitutions.

 

[Gib Z]

Note: $$\log_a b^x = x \log_a b$$ where a, b and x are real numbers, (a,b) > 0.