How Do You Find the Antiderivative of \( \frac{2}{2x+1} \)?

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    Antiderivative
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Discussion Overview

The discussion revolves around finding the antiderivative of the function \( \frac{2}{2x+1} \). Participants explore different methods and approaches to solve this problem, including substitution techniques.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks how to determine the antiderivative of \( \frac{2}{2x+1} \).
  • Another participant suggests that the antiderivative might be \( \frac{1}{2}(2x+1) \).
  • A different participant proposes using u-substitution with \( u = 2x + 1 \) as a method to solve the integral.
  • A follow-up question seeks clarification on whether the expression \( \frac{2}{2x+1} \) is indeed \( \frac{2}{2x+1} \) and asks about the antiderivative of \( \frac{1}{u} \) or \( \int \frac{du}{u} \).

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the antiderivative, as multiple approaches and interpretations are presented without agreement on a definitive solution.

Contextual Notes

Participants express uncertainty regarding the correct form of the antiderivative and the application of substitution methods, indicating potential limitations in their understanding or assumptions about the integral.

afcwestwarrior
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2/2x+1

how do i figure this out
 
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is it 1/2 (2x+1)
 
Solve it by u-substitution where u=2x+1
 
afcwestwarrior said:
2/2x+1

how do i figure this out
Is that [tex]\frac{2}{2x+1}[/tex]?

Then along the lines of Feldoh's comment, what is the antiderivative or integral of 1/u

or [tex]\int\frac{du}{u}[/tex]
 

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