I see your point, but as it is stated in the article, it is one of those techniques that require practice, and time to mature. And like it mentions, it's a bit like chess...when you're presented with some troubling integral, you can parametrize it in a number of ways. Most will bring you back to the beginning (like with the standard integration by parts), but the right one will make your life much easier.
It can be frustrating when math does not have any clear single path, but that's just the nature of the beast. In the beginning you'll just have to explore all the paths, but do that a couple of hundred times, and you'll start to notice patterns and what will work / what will not. Kind of like chess, where a good chess player can think N moves ahead in time.
It can be frustrating when math does not have any clear single path, but that's just the nature of the beast. In the beginning you'll just have to explore all the paths, but do that a couple of hundred times, and you'll start to notice patterns and what will work / what will not. Kind of like chess, where a good chess player can think N moves ahead in time.