What is Lonewolf's proposed method for integrating Ln[x]dx?

  • Context: Graduate 
  • Thread starter Thread starter PrudensOptimus
  • Start date Start date
  • Tags Tags
    Dx Integrate Ln
Click For Summary

Discussion Overview

The discussion revolves around the integration of the function Ln[x]dx, particularly focusing on the interpretation of [x] as the greatest integer function. Participants explore various methods and implications of this integration, considering both analytical and numerical approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using integration by parts on the function considered as 1*ln(x).
  • Another participant provides a link to an online integral calculator, which gives a specific answer for the integral of ln(x) but does not clarify if it applies to the greatest integer function.
  • There is uncertainty about whether [x] refers to the greatest integer function, with one participant expressing doubt about the existence of a closed form for the integral of ln[x] when [x] is interpreted this way.
  • A participant proposes breaking the integral into a summation, noting that [x] remains constant between integer intervals, leading to a sum of simpler integrals, which they attribute to Lonewolf's method.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of [x] or the feasibility of finding a closed form for the integral. Multiple competing views and methods are presented without resolution.

Contextual Notes

The discussion highlights the ambiguity in the notation used and the potential limitations in deriving a closed form for the integral based on the interpretation of [x].

PrudensOptimus
Messages
641
Reaction score
0
Integrat Ln[x]dx!
 
Physics news on Phys.org
Consider it as 1*ln(x) and use parts.
 
If you don't feel like doing it, you can always use:

http://integrals.wolfram.com/index.en.cgi

It gives the answer:

[tex] -x + x \ln x[/tex]
 
Is [x] greatest integer function??
 
Hmm, didn't consider that. I'm not sure there'd be a closed form expression for [itex]\int ln[x] dx[/itex]
where [itex][x][/itex] is the next greatest integer function. It'd be easy enough to get a numerical answer if the interval was specified though.
 
Last edited:
You could break the integral into a summation. [x] is constant between intervals of integers, so you end up with a sum of trivial integrals.

I think this is what Lonewolf is proposing (please excuse my ignorance!)

Regards,
Sam
 

Similar threads

Undergrad Integrating 1/x with units (logarithm)
  • · Replies 15 ·
Replies
15
Views
4K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
4K
MHB Indeterminate Integration with Integration Constant
  • · Replies 6 ·
Replies
6
Views
2K
MHB Definite integral challenge ∫ln(2−2cosx)dx=0
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Non solvable integral? (dx/dt)^2 dt
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Gaussian integral by differentiating under the integral sign
  • · Replies 19 ·
Replies
19
Views
5K
Undergrad PF Integral Bee: Share Interesting/Quirky Integrals!
  • · Replies 1 ·
Replies
1
Views
1K
MHB Improper integral of an even function
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How do I apply the method of steepest descents to this integral?
  • · Replies 1 ·
Replies
1
Views
3K
MHB 15.1.34 Evaluate triple integral
  • · Replies 2 ·
Replies
2
Views
2K