Integrating Natural Logarithms: A Scientific Approach

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Discussion Overview

The discussion revolves around the integration of the natural logarithm function, specifically focusing on the integral of ln(x). Participants explore the method of integration by parts, detailing the steps involved in the process.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks for the integral of ln(x).
  • Another suggests using integration by parts, proposing the expression x*ln(x) - x as the result.
  • A request for a complete demonstration of the integration process is made.
  • Steps for integration by parts are provided, including the definitions of u and dv/dx.
  • A participant expresses confusion about a specific step in the integration process, questioning whether ∫u*dv/dx should equal ∫1.
  • Subsequent messages indicate that the participant who raised the question later found their mistake.
  • Another participant acknowledges the confusion and expresses relief that the issue was resolved.

Areas of Agreement / Disagreement

The discussion appears to have a general agreement on the method of integration by parts, but there is a moment of uncertainty regarding a specific step in the process. The initial confusion is resolved by the participant who questioned it.

Contextual Notes

Some assumptions about the integration process and the definitions of variables are not explicitly stated, which may affect the clarity of the discussion.

Who May Find This Useful

Students or individuals seeking assistance with integration techniques, particularly those involving logarithmic functions.

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what is the integral of lnx?
 
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Try writing it as 1*ln(x), then integrate by parts. (Should get x*ln(x)-x).
 
could you show me the entire way?
 
Sure

∫1*ln(x)dx

du/dx = 1
v = ln(x)

u = x
dv/dx = 1/x

Now, integrating by parts:

∫1*ln(x)dx = u*v - ∫u*dv/dx
= x*ln(x) - ∫dx
= x*ln(x) - x (+ C to be pedantic)
 
i got it, thanks.

edit: just one problem should this ∫u*dv/dx=∫1
 
Last edited:
Originally posted by loop quantum gravity
i got it, thanks.

edit: just one problem shouldn't this be ∫u*dv/dx=∫1 ?
lonewolf i think i am wrong but i need your verification on that.
 
never mind i found my mistake.
 
Oops, sorry LQG, I wasn't ignoring you intentionally. Glad you figured it out anyway :smile:
 

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