Can somebody tell me what this means? dy/dx means a small change in y with respect to a small change in x. du/u means a small change in u with respect to no change in u?

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- Mar 15th 2010, 09:02 PM #1

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- Mar 15th 2010, 09:09 PM #2

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- Mar 15th 2010, 09:11 PM #3
It's just a shorthand way of writing the chain rule in reverse (for integration, the reverse process of differentiation).

$\displaystyle \int{f\left(g(x)\right)\,g'(x)\,dx} = \int{f(u)\,\frac{du}{dx}\,dx} = \int{f(u)\,du}$ by making the substitution $\displaystyle u = g(x)$.

In your case, $\displaystyle f\left(g(x)\right) = \frac{1}{g(x)}$.