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Are the following integrals equivalent:

Integral from 0 to 5 of dx / x

and

Integral from 0 to 5 of dx / (x + dx)

What about

Integral from 0 to 5 of dx / (x + 2dx + dx^2)

???

If they are all equivalent, why? (I have an intuitive answer, but it has 0 mathematical foundation). Or are they not all the same? Can someone explain this strongly?

Thank you!

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# Homework Help: Differentials under differentials in integrals

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