Choosing an Integration Method
We've been learning the different methods of integration in a very artificial environment. We know that if we're in the "Integration by Substitution" section, we use substitution. If we're in the "Integration by Parts" section, we use integration by parts.
In the real world (by which we mean on exams), the directions probably won't say which method to use—we'll have to figure that ourselves.
The more we practice, the better we'll get at figuring out which method to use. We won't even have to think about it. In the meantime, we have some hints.