How Is the Integral of Natural Log of x Calculated?

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SUMMARY

The integral of the natural logarithm of x, denoted as ∫ln(x)dx, is calculated using integration by parts. The anti-derivative is expressed as x(ln x - 1). This method involves selecting u = ln(x) and dv = dx, leading to the derivation of the result through the application of the integration by parts formula.

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  • Understanding of integration by parts
  • Familiarity with natural logarithm properties
  • Basic calculus concepts
  • Knowledge of anti-derivatives
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  • Study the integration by parts formula in detail
  • Explore examples of integrating logarithmic functions
  • Learn about the properties of natural logarithms
  • Practice calculating anti-derivatives of various functions
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Students and educators in calculus, mathematicians, and anyone seeking to understand the integration of logarithmic functions.

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can someone please explain this to me?
 
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The anti-derivative of the natural log of x is x(ln x -1). This can be seen by integrating the natural log through integration by parts, letting dv=dx and u= ln x.

Btw, welcome to Physicsforums!
 

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