Why Does ∫ln(x) dx Include dx?

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    Derivative Integral
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SUMMARY

The integral of the natural logarithm function, ∫ln(x) dx, includes "dx" to indicate the variable of integration, which is x in this case. This notation is consistent with differentiation, where "dx" appears in the derivative notation dy/dx, signifying the relationship between the variables. Understanding this notation is crucial for correctly interpreting integrals and derivatives in calculus.

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  • Basic understanding of calculus concepts, specifically integration and differentiation.
  • Familiarity with the natural logarithm function, ln(x).
  • Knowledge of integral notation and its components.
  • Experience with variable representation in mathematical expressions.
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  • Study the Fundamental Theorem of Calculus to understand the relationship between differentiation and integration.
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find ∫ln x dx. i can't work this out but i know its integration. why is there a dx here. there is usually no dx when i am differentiating something
 
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markosheehan said:
find ∫ln x dx. i can't work this out but i know its integration. why is there a dx here. there is usually no dx when i am differentiating something

All integrals are written with dx at the end, it's read as "the integral of the function ln(x) with respect to x".

And all derivatives have the same, have you never noticed that "dx" in dy/dx?
 

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