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

In summary, the conversation discusses the integration of ln[x]dx using the parts method. However, it is suggested to use a website like integrals.wolfram.com for the answer. The conversation also mentions the possibility of using the greatest integer function [x] in the integral, but it may not have a closed form expression. It is suggested to break the integral into a summation to calculate a numerical answer.
  • #1
PrudensOptimus
641
0
Integrat Ln[x]dx!
 
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  • #2
Consider it as 1*ln(x) and use parts.
 
  • #3
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]
 
  • #4
Is [x] greatest integer function??
 
  • #5
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:
  • #6
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
 

What is the integration formula for Ln x?

The integration formula for Ln x is ∫ Ln x dx = x Ln x - x + C, where C is the constant of integration.

Can Ln x be integrated using substitution?

Yes, Ln x can be integrated using substitution. The most common substitution used is u = Ln x, which results in du = 1/x dx.

What is the domain for the integration of Ln x?

The domain for the integration of Ln x is (0, ∞). This means that the natural logarithmic function can only be integrated for positive values of x.

Is there a specific technique for integrating Ln x?

Yes, there is a specific technique for integrating Ln x. It is known as integration by parts, which involves breaking down the integrand into two parts and using a specific formula to integrate them.

What are some real world applications of integrating Ln x?

Integrating Ln x is commonly used in various fields of science and engineering, such as in the study of population growth, radioactive decay, and chemical reactions. It is also used in economics for calculating compound interest and in statistics for calculating probabilities.

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