Struggling with an Integral Involving Natural Logarithms?

  • Thread starter Thread starter kennis2
  • Start date Start date
  • Tags Tags
    Hard Integral
Click For Summary

Homework Help Overview

The discussion revolves around an integral involving natural logarithms, specifically the integral of (1+ln(x))/xln(x) and later a revised integral of (sqrt(1+ln(x)))/xln(x). Participants are exploring the complexities of these integrals and the methods to approach them.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the differentiation of xln(x) as a potential approach, with one suggesting the use of the product rule. There is also a question about the relevance of the integral to finding arc length, and a suggestion to use substitution for simplification.

Discussion Status

The discussion is active, with participants providing hints and clarifications. There is an acknowledgment of a mistake in the original integral, prompting a revised question. Multiple interpretations of the problem are being explored, and guidance has been offered without reaching a consensus.

Contextual Notes

Participants are working under the constraints of homework rules, and there is a focus on ensuring clarity in the expression of the integral. The original poster's confusion about the integral setup has been noted.

kennis2
Messages
8
Reaction score
0
(edited need help) hard integral to me but you?

I tried much but i couldn't resolve..
Integral of (1+ln(x))/xln(x) dx
thanks =)
 
Last edited:
Physics news on Phys.org
Hint:
What is
[tex]\frac{d}{dx}(xlnx)=?[/tex]
 
its 1/x right?
 
Last edited:
No, you must use the product rule:
[tex]\frac{d}{dx}(xln(x))=1*ln(x)+x*\frac{1}{x}=ln(x)+1[/tex]
What does that tell you?
 
oh you are right!
I know the answer then, BUT
I WROTE MY EXERCISE BAD SORRY HERE GO AGAIN
integral of (sqrt(1+ln(x)))/xln(x) dx
 
Last edited:
Does this pertain to finding the arc length of a function? Also, try writing it out in latex, you'll probably get more responses.
 
is this the question??

[tex]\frac{\sqrt{1+\ln x}}{x \ln x} dx[/tex]?

in which case substitute ln x = u and solve away!
 

Similar threads

Replies
2
Views
1K
Replies
14
Views
3K
  • · Replies 18 ·
Replies
18
Views
2K
Replies
7
Views
3K
  • · Replies 7 ·
Replies
7
Views
1K
Replies
1
Views
3K
Replies
28
Views
2K
  • · Replies 14 ·
Replies
14
Views
4K
Replies
30
Views
2K
Replies
5
Views
3K