compute
I don’t remember the equations for integration by parts and haven’t used them in years. However, when I saw this, I immediately started scribbling on the whiteboard by my bed, thinking:
“Okay, so start with (x^2)log(x). Differentiating that gives two times the target, but also gives us a spare x we’d need to get rid of. So the answer is (0.5)(x^2)log(x) - (x^2)/4.”
So I actually think you’re right in general but wrong on this specific example: getting a deep sense for what you’re doing when you’re doing integration-by-parts would be a more robust help than rote memorization.
(Though rote memorization and regular practice absolutely have their place; if I’d done more of those I’d have remembered to stick a “+c” on the end.)
Good choice of topic.
Everyone has their own needs and tolerances, so I won’t presume to know yours . . . and if you’re trying to build daily habits, “every morning” is probably easier to reliably schedule than “every night” . . . but still, sleep is a big deal, especially for intellectual work. If you’re not unsually good at going without for long stretches, and/or planning to turn in before 10pm to compensate . . . you might benefit from a slightly less Spartan schedule.
What kind(s) of writing do you want to be able to produce?
I’m curious how you plan on practicing your rationality, and how you intend to measure improvement. As far as I can tell our subculture has been trying to figure this out for a decade and change, with sharply limited success.