Why can't we just integrate a simple function?

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SUMMARY

The discussion centers on the integration of the function ##\ln(5 - 2x)## and the significance of the anti-derivative in calculus. Participants clarify that the integral represents the anti-derivative, and the multiplier ##-1/2## arises during differentiation. Understanding this relationship is crucial for correctly applying integration techniques in calculus.

PREREQUISITES
  • Understanding of calculus concepts, specifically integration and differentiation.
  • Familiarity with logarithmic functions, particularly natural logarithms.
  • Knowledge of anti-derivatives and their properties.
  • Basic algebra skills for manipulating expressions.
NEXT STEPS
  • Study the properties of logarithmic differentiation.
  • Learn about the Fundamental Theorem of Calculus.
  • Explore integration techniques involving substitution and their applications.
  • Practice problems involving the differentiation of logarithmic functions.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus, as well as anyone seeking to deepen their understanding of integration and differentiation concepts.

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)##?
 
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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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