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

1. Nov 14, 2007

### poopforfood

1. The problem statement, all variables and given/known data

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

2. Relevant equations

n/a

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

2. Nov 14, 2007

### 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.

3. Nov 14, 2007

### poopforfood

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

4. Nov 14, 2007

### Dick

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

5. Nov 21, 2007

### 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.

6. Nov 21, 2007

### Gib Z

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