I Why can't we just integrate a simple function?

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The discussion centers on understanding the integration of a function and the concept of the anti-derivative. Participants explore why the integral of a function, specifically ##\ln(5 - 2x)##, involves a multiplier of ##-1/2##. The relationship between differentiation and integration is emphasized, highlighting that the integral is essentially the anti-derivative. Clarification is provided on how differentiating the logarithmic function leads to the appearance of the multiplier. The conversation concludes with a sense of understanding regarding the integration process.
NODARman
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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)##?
 
Your question is where does the ##-1/2## multiplier come from?
 
PeroK said:
The integral is the anti-derivative. What happens when you differentiate ##\ln(5 - 2x)##?
Just got it 🙂 👍
 

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