How Do You Solve This Challenging Integral Puzzle?

  • Context: Graduate 
  • Thread starter Thread starter 54stickers
  • Start date Start date
  • Tags Tags
    Integral Puzzle
Click For Summary

Discussion Overview

The discussion revolves around solving a challenging integral presented by a participant. The integral involves logarithmic functions and requires a suitable substitution for evaluation. The scope includes mathematical reasoning and problem-solving techniques related to integrals.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in solving the integral \(\int^{1}_{0}\frac{dx}{\sqrt{log(\frac{1}{x})}}\) and seeks assistance.
  • Another participant suggests using the substitution \(u = \sqrt{Log(\frac{1}{x})}\) as a potential approach.
  • A third participant reminds others that \(\log(1/x) = - \log x\), which may be relevant for the substitution process.
  • A later reply indicates that the suggested substitution was successful for the original poster, expressing a sense of realization for not trying it sooner.

Areas of Agreement / Disagreement

Participants generally agree on the validity of the substitution approach, but there is no explicit consensus on the overall solution to the integral, as the discussion does not delve into the final evaluation.

Contextual Notes

The discussion does not clarify the implications of the substitution or any potential limitations in the approach taken. There may be unresolved steps in the evaluation of the integral following the substitution.

54stickers
Messages
28
Reaction score
0
I have an integral in my math text that I cannot seem to tackle, help would be appreciated. thanks! I am not really sure where to start.

\int^{1}_{0}\frac{dx}{\sqrt{log(\frac{1}{x})}}
 
Physics news on Phys.org
Try the substitution u = \sqrt{Log(\frac{1}{x})}
 
Before you substitute anything, remember that ##\log(1/x) = - \log x##.
 
The substitution worked perfectly, Thanks!

I am going to pinch myself for not trying that earlier.
 

Similar threads

Graduate Challenging integral involving exponentials and logarithms
  • · Replies 14 ·
Replies
14
Views
3K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Multiplying divergent integrals using Hardy fields approach
  • · Replies 3 ·
Replies
3
Views
2K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
High School I need to check if I am right solving this integral
  • · Replies 2 ·
Replies
2
Views
2K
MHB Indefinite integral in division form
  • · Replies 1 ·
Replies
1
Views
2K
High School Integration by Parts, an introduction I get confused with
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K