First off, I'd like to say that I love your videos! The reason I am writing: I ran across Feynman's "differentiation under the integral" trick years ago when I went on a bit of a Feynman kick (recommend! a brilliant man...). It recently popped up again on my fb here: https://medium.com/cantors-paradise/differentiation-under-integral-sign-w-examples-9afbf121d668 If you haven't already, his technique might be worth a look, and perhaps a video? Just a thought.
Anyway, keep on doing good things!