I’ve never taught Calculus, and I find myself struggling with this mistake…

…in a good way. Here’s what’s want through my head:

- Oh, God, integration.
- How would I solve it? Is there any way that I can avoid integrating by parts? (Yeah: transform the numerator to (x-1)+1.)
- Oh, shoot, how do you integrate by parts anyway? It’s vdu – uduvuvvvvvuuu or whaaaaa???
- [Googles integration by parts]
- [Solves it using integration by parts]
- Good Lord I don’t like integrating by parts.
- What did this kid do wrong?
- It looks like they ended up with a square root instead of a square?
- That makes sense. People often make association mistakes when they’re working on a problem where they have to keep in mind a bunch of moving parts.

I think that working through math mistakes like this one would be a great way to prepare for a new course.

(Hey! Someone should start collecting and organizing these so that they’re available to new teachers…)