# Introductory U-substitution

We’ve been doing a little bit of work in the integration chapter of our calculus book. Today the topic was u-substitution. I was expecting the topic to produce a great deal of confusion, but things went pretty smoothly. There will be plenty of time for confusing integration problems later, I guess, ha!

When my son got home from school tonight I had him try out three problems from the u-substitution section. The first two are straightforward and the third is a bit of a surprise.

Here’s the first one: $\int (1 - 2y)^{13} dy$

For the next problem I chose a trig integral: $\int \cos(x)^4 \sin(x) dx$

Finally, I chose a problem that isn’t obviously a u-substitution problem when you look at it: $\int x \sqrt{x - 1} dx$

Again, I was worried that we’d get off to a bit of a rocky start, but thinks went well today. Going to have him work through a bunch of problems tomorrow to get a little more u-substitution practice.