It's Obvious... Not: Knowing When not to do the Math

I'm still studying for quals. I got stuck for awhile on problem 2.11 of Griffith's Introduction to Quantum Mechanics first edition. The problem involves manipulating raising and lowering operators to perform a normalization. The problem I was having was doing too much of the math too early. I tried to expand all the operators and got stuck. I tried to apply integration by parts as the book suggests and applied it to the wrong term the first time, and carried the operation too far on a second try. The series of conservative steps that finally did the trick is shown in the video below.