Studying techniques of integration with 5 integrals

We had a 2 hour delay for school today, so we had a little extra time this morning to talk calculus. My plan was to spend all of March on techniques of integration, but we are a little ahead of schedule having already covered integration by parts and partial fractions.

Today my son moved on to a “techniques of integration” section in Stewart and was looking at a bunch of integrals without knowing what techniques to use. After he worked for a bit we talked about the first 5 problems from the section:

(1) A substitution integral with trig functions

(2) An integration by parts problem:

(3) A slightly disguised arcangent problem

(4) A sort of silly u-substitution problem

(5) A partial fractions problem