How Do You Integrate 1/[xlog(x)]?

  • Context: Undergrad 
  • Thread starter Thread starter euclid3.14
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Discussion Overview

The discussion revolves around the integration of the function 1/[x log(x)], exploring various methods and substitutions to arrive at the integral's solution. Participants engage in technical reasoning and mathematical manipulation related to integration techniques.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about integrating the function and mentions a potential answer of log[log(x)], but is unsure how to derive it.
  • Another participant suggests substituting u=log(x) as a method to simplify the integral.
  • A subsequent post elaborates on the substitution, showing the transformation of the integral into a simpler form, ultimately leading to log[log(x)].
  • Several posts reiterate the integral transformation using different notations, indicating a focus on the mathematical representation of the integration process.
  • One participant acknowledges a mistake in their earlier post, indicating a collaborative environment where corrections are made.

Areas of Agreement / Disagreement

Participants generally agree on the substitution method and the resulting integral form, but there is no explicit consensus on the clarity of the initial confusion expressed by the first participant.

Contextual Notes

Some participants' posts contain variations in notation and formatting, which may lead to misunderstandings. The discussion does not resolve the initial confusion about the integration process.

Who May Find This Useful

Individuals interested in integration techniques, particularly those dealing with logarithmic functions, may find this discussion beneficial.

euclid3.14
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This is doing my head in!

I split it to 1/x * 1/log(x) and got the intergral = 1 + the intergral when using intergration by parts. :cry:

I know the answer is log[log(x)] but have no idea how you get log of a log.

Got a feeling the answer is going to really obvious!
 
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Substitute u=log(x)
 
log(x) = u, u=exp(x), x du = dx.
intergral becomes exp[-u] 1/u exp du
= 1/u du
= log u
= log[log(x)]

Cheers! :biggrin:
 
\int{frac{1}{x\ln{x}}}\d x=\int{frac{1}{\ln{x}}}\d \ln{x}
 
[tex]\int{frac{1}{x\ln{x}}}\d x=\int{frac{1}{\ln{x}}}\d \ln{x}[\tex][/tex]
 
[tex]\int{frac{1}{x\ln{x}}}\d x=\int{frac{1}{\ln{x}}}\d \ln{x}[/tex]
 
Do you mean?

[tex]\int\frac{1}{x\ln{x}}}dx=\int\frac{1}{\ln{x}}d\ln{x}[/tex]

You can click on the above for the code that generated it.

You know you can preview posts before you submit. You can also edit and delete!
 
I see. Sorry for making a big mess here.
 

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