hey Dr. Weber! I just wanted to give feedback that I'm not so confident in the way you explained 27:30 I think it would've been better to explain that with a u-sub, you have to get `dx` replaced with `du` and that it would've made for sense that you divided by 8 with the `du` so that it'd look like: `1/8*du = x*dx`, that way it would've made for much more clarity as to explain why and how 1/8 goes outside the integral like that.