Why can't we just integrate a simple function?

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Discussion Overview

The discussion revolves around the process of integrating a function, specifically focusing on understanding the correct application of integration techniques and the role of anti-derivatives. Participants are exploring the reasoning behind certain steps in integration, including the appearance of specific multipliers in the results.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for clarification on why a particular integral is considered correct, referencing an attachment for context.
  • Another participant states that the integral represents the anti-derivative and poses a question regarding the differentiation of ##\ln(5 - 2x)##.
  • A different participant seeks to understand the origin of the ##-1/2## multiplier in the context of the integral.
  • One participant reiterates the anti-derivative concept and again questions the differentiation of ##\ln(5 - 2x)##, indicating they have reached an understanding.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints regarding the integration process and the specific details of differentiation, with no clear consensus reached among participants.

Contextual Notes

Participants reference specific mathematical expressions and concepts, but the discussion does not resolve the underlying assumptions or steps involved in the integration process.

NODARman
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TL;DR
.
Can anyone explain to me why the second one is the right?
(See the attachment)
PXL_20221016_130317184.jpg
 
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The integral is the anti-derivative. What happens when you differentiate ##\ln(5 - 2x)##?
 
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Your question is where does the ##-1/2## multiplier come from?
 
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PeroK said:
The integral is the anti-derivative. What happens when you differentiate ##\ln(5 - 2x)##?
Just got it 🙂 👍
 

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