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

  • #1

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

 

Answers and Replies

  • #2
492
1
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
well you see there bob im not too sure how to get started and what to do with the ln
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
619
If you don't know what to do, then you don't know it diverges, right? Try a substitution u=ln(x).
 
  • #5
92
0
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
Gib Z
Homework Helper
3,346
5
Note: [tex]\log_a b^x = x \log_a b[/tex] where a, b and x are real numbers, (a,b) > 0.
 

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