Can you integrate ln(x + x^2) using integration by parts?

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Discussion Overview

The discussion centers around the integration of the function ln(x + x²), specifically exploring the method of integration by parts and the correct application of differentiation. Participants are clarifying the distinction between integration and differentiation in this context.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the result of integrating ln(x + x²) is (1 + 2x)/(x + x²), but there is uncertainty about whether this is an integration or differentiation result.
  • One participant suggests that to check the integration result, one should differentiate it to see if it returns to ln(x + x²).
  • Another participant emphasizes the need to clarify whether the task is integration or differentiation, indicating that the logarithm can be split using properties of logarithms.
  • There is a suggestion to use integration by parts as a standard method for integrating ln functions, but the necessity to first factor the logarithm is also highlighted.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct integration of ln(x + x²), with multiple viewpoints presented regarding the method and the interpretation of the original question.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the integration process and the definitions of the functions involved. The mathematical steps for integration remain unresolved.

DigiDigi
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Integration of ln(x + x^2) is it (1+2x)/(x+x^2)?
 
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There's always an easy check: differentiate the result.
It should give you ln(x + x²) back.
 
Hi DigiDigi! :smile:
DigiDigi said:
Integration of ln(x + x^2) is it (1+2x)/(x+x^2)?

If you mean differentiation, then yes that's the correct application of the chain rule. :wink:

(What is worrying you about that? :confused:)
 
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DigiDigi said:
Integration of ln(x + x^2) is it (1+2x)/(x+x^2)?

Are you trying to differentiate or integrate?

If it's the former, that's correct.

If it's the latter, it isn't. But it's easy to do. Hint: ln(ab) = ln a + ln b. Factorise!
 
I try to integrate. Looks like I make mistake and differentiate it. We integrate using integration by parts?
 
DigiDigi said:
I try to integrate. Looks like I make mistake and differentiate it. We integrate using integration by parts?

Yes. The standard way to integrate ln x is to use integration by parts. Do you know how to do this?

But first, do what I said in the previous post to split the logarithm up.
 

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