In answers on this site often the word "u-substitution" appears. Why this is called u-substitution? Is it the same as integration by substitution?

(I never heard this term before and I'm not sure if we have it in my native language)

Edit: I myself find the question rather stupid. However, I constantly was thinking "maybe I'm missing something". From the comments I can see that I'm not the only one who gets confused if something simple like "integration by substitution" is called something else like "u-substitution". Especially, if there is "u-substitution" maybe there is "v-substitution" and "t-substitution", and ... . All things which I might never heard of.

So I guess I leave this question here for everybody else who does not know what u-substitution is.

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    $\begingroup$ It seems to be American slang; I remember being confused by it too... $\endgroup$ – J. M. isn't a mathematician May 8 '11 at 7:56
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    $\begingroup$ This question is answered by the last sentence of the introduction to the Wikipedia article, which is the third Google result (for me) for "u-substitution": en.wikipedia.org/wiki/Integration_by_substitution $\endgroup$ – Qiaochu Yuan May 8 '11 at 8:23
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    $\begingroup$ @J.M. mathematics slang? Nice :) Soon we'll be calling $C^{\infty}$ functions "smoothies" and prime numbers "lil' ninjas" $\endgroup$ – Stijn May 8 '11 at 8:28
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    $\begingroup$ "Smoothies" I can understand, but why "lil' ninjas"? $\endgroup$ – yunone May 8 '11 at 8:45

I think it's because the letter $u$ is often used, for some reason, to denote the name of the function that is used in the substitution.

edit and indeed, as Qiaochu Yuan mentioned, we're talking about integration by substitution.

  • $\begingroup$ And it is the same as integrate by substitution? $\endgroup$ – Fabian May 8 '11 at 7:52
  • $\begingroup$ @Fabian: yes, it is. $\endgroup$ – Qiaochu Yuan May 8 '11 at 8:21

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