Euler’s substitutions in indefinite integrals are the next thing introduced after rational integrals, trigonometric integrals, and root integrals. This means that most students won’t have the pleasure of encountering them, and I haven’t included them in my Course on Indefinite Integrals.
However, there remains quite a large group of students in mathematical fields who have to deal with Euler’s substitutions, and I invite these (and the curious) to join. I will discuss all three types of Euler’s substitutions (in this post I will cover the first type) and provide one example for each.