A famous technique in the modification of integrands is the set of “euler substitutions” that provide substitutions for the structure

$$\sqrt{ax^2 +bx+c}$$

That is a fairly common occurence in integration.

I looked on the wikipedia page, and did not find any reference to where Euler introduced them.

Does anybody know in which text euler introduces these substitutions?

  • 1
    $\begingroup$ I'd be surprised if Euler were really the first person to deal with this: surely the Bernoullis could do this kind of thing, considering the far fancier stuff they did...??? $\endgroup$ Mar 2, 2023 at 21:46
  • $\begingroup$ that's true. I just assumed euler invented these subs based on the name. $\endgroup$
    – Hisham
    Mar 2, 2023 at 23:59


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