MHB Why Does ∫ln(x) dx Include dx?

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The integral of ln(x) is expressed with "dx" to indicate the variable of integration, meaning it is the integral of ln(x) with respect to x. This notation is standard in calculus, similar to how derivatives are represented with "dx" in dy/dx. The presence of "dx" clarifies the relationship between the function and the variable being integrated. Understanding this notation is crucial for correctly interpreting calculus operations. The discussion emphasizes the importance of recognizing "dx" in both integration and differentiation.
markosheehan
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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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