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

## 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

## The Attempt at a Solution

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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.

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

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

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