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.)
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.)