I glanced through "easy cases", and the "guessing the solution" part looks more like "we somehow magically know that the solution is among these 3 or 5 possibilities, now we eliminate obviously wrong answers and lo, we found a solution".
Seriously, just look at the treatment of Gaussian integral. They wonder if the solution is sqrt(pi alpha) or sqrt(pi/alpha). Then they rule out the first possibility. Yeah, that's fine, but why sqrt and pi at all? Why not sin and e? Or gamma function and ... oh well this actually is a gamma function, but nevermind.
Guessing is easy, if you already know the solution.
Seriously, just look at the treatment of Gaussian integral. They wonder if the solution is sqrt(pi alpha) or sqrt(pi/alpha). Then they rule out the first possibility. Yeah, that's fine, but why sqrt and pi at all? Why not sin and e? Or gamma function and ... oh well this actually is a gamma function, but nevermind.
Guessing is easy, if you already know the solution.