Last night I tweeted about starting partial fractions with my son an got a really neat response from Jennifer Vibber:

I teach lots more of partial fraction decomposition to my calc 3 seniors the following year. Repeated linear, quadratic , 3 distinct linear… I also give this out in BC to test them on look alikes… pic.twitter.com/BePcg3tNpR

Tonight I decided to have my son work through Vibber’s integrals and talk about the technique of integration needed to solve the problem. He’s been away hiking in the White mountains for a week, so calculus wasn’t necessarily the top thing on his mind. Even with that break, though, it was interesting to see how he approached all of these problems and working through the list made for a great integration review:

Once we were done we revisited two of the problems to see if he could figure them out with a little bit more time. Here’s the first one:

This one was a bit more complicated, but he ended up finding a substitution that worked and led to a really nice solution:

Thanks to Jennifer Vibber for sharing these nice problems last night!