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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Is any possible u substitution legal so long as you replace dx with an equivilent form of du?

A logarithm is just a misspelled algorithm.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

I mean it makes sense you could replace x^2 with u as a sort of notation for x^2 but for instance, could you replace any function with any functon so long as you find the du equivilent for dx? (or whatever the original variable of integration was)

Like ln u = cos x, ln u gets bigger as u gets bigger, but cos x fluctuates between 1 and -1. My book discussed many types of substitutions you can do, but never stops to explain what substitutions you can't use.

A logarithm is just a misspelled algorithm.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

If you want to sub for cos x like that, then u = e^cos(x), so the domain of u is restricted by the range of e^cos(x). Thus, ln(u) is restricted by cos(x).

But with an example like this, du = -sin(x)e^cos(x)dx.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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