I hope you find this helpful! Table of contents is below for you to follow along :)

Worksheet:
https://people.math.sc.edu/josephcf/Teaching/TA142/Files/Handouts%20and%20Worksheets/U-Substitution.pdf

TABLE OF CONTENTS:
0:00 - Intro (worksheet link in description)
1:37 - Problems 1 & 2 (Basic Substitutions)
5:41 - Solutions to Problems 1 & 2
5:42 - Problems 3 & 4 (dx Cancellations)


10:55 - Solutions to Problems 3 & 4
11:15 - Problem 5 (dx Cancellation with arctan)
13:16 - Solution to Problem 5
14:12 - Problems 6 & 7 (x^n * f(x^n+1) integrals)

17:59 - Solutions to Problems 6 & 7
19:55 - Problems 8 & 9 (More complex x^n * f(x^n+1) integrals)
24:20 - Solutions to Problems 8 & 9
25:00 - Problem 10 (More complex x^n * f(x^n+1) integrals)
26:54 - Solution to Problem 10
26:57 - Problem 11 (Solve for x in terms of u)
32:21 - Solution to Problem 11 (see comments)
33:07 - Problem 12 (Solve for x in terms of u - more complex)
37:45 - Solution to Problem 12
37:48 - Problem 13 (Solve for x in terms of u)
41:30 - Solution to Problem 13
41:36 - Deriving the integral of sec(x)tan(x) using u-substitution