Memorable Timestamps:
1:00 Standard Integrals
13:35 Introducing Symmetry
28:02 Introducing Awkward Trig Computations
36:19 Introducing Absolute Value Cases
44:31 A Foolish Trap
Memorable Timestamps:
0:55 The Beginning
3:52 Bringing in that Constant
13:46 Intermediate Case of U-substitution
22:17 Double U-Substitution
29:37 Strategizing with U-Substitution (from u=x^4 to u=x^2)
35:22 Dealing with Bounds in U-Substitution
45:50 Hidden Symmetry!!
49:11 Area of a Partial Circle
1:06:44 A Bound with Infinity
Memorable Timestamps:
0:22 Intro to DI/Ladder Method
8:56 Reverse Product Rule Trick
17:00 Forced U-Substitution
20:47 Recursive Integration by Parts
28:47 Definite Integrals + Warnings
39:41 Funky Arctan Integral
51:34 An Integral with Zero Substitution
Memorable Timestamps:
00:36 First Integral
2:33 Introducing Wallis Trick
7:09 Double Angle Identity
16:10 Definite Integral Example
18:48 Dealing with Tanx and Secx
23:00 Simplifying with Sines and Cosines
23:57 Tan(x) Trick
25:00 Geometric Polynomial Division with Tan(x)
34:42 Sum Angle Identity Trick
49:20 An Absolute Reminder
53:50 REMEMBER YOUR TRIG IDENTITY!!
55:00 Trig Conjugation
56:31 Somethin sus...
59:04 The Process of Sec^3(x)
Memorable Timestamps:
0:37 Intro to the Concept of Trig-Sub
8:03 Beware of Fake Trig-Subs!!
11:25 A Fractional Exponent Trig-Sub
13:21 Another Fake Trig-Sub!!!
16:14 Dealing with Constants
20:40 An Awkward Trig-Sub Case
24:29 Non-Radical Trig-Sub
27:00 An Integral with a Sneaky Trick
32:22 Completing the Square
46:28 A Beautiful Monstrous Trig-Sub Integral
53:41 An Intimidating Ugly Trig-Sub Integral
58:07 Another Fake Trig-Sub, but also Non-Radical
1:01:23 Advanced Trig-Sub (Special Cases)
Memorable Timestamps:
0:44 Geometric Polynomial Division
2:49 The Purpose of Zero Substitution
4:57 Basics of Heaviside Method
7:47 Force an Arctan!!
12:35 Advanced Heaviside Method (Non-Linear Polynomial)
21:00 DU-ing the Numerator
25:02 Advanced Heaviside Method (Powered Linear Polynomial)
32:51 Heaviside Sprinting Example!!
34:17 Another DU-ing the Numerator Concept
38:45 Dummy Variable Heaviside Method
45:56 Basic U-Sub Examples
48:49 Another Advanced Heaviside Method (Non-Linear Polynomial)
57:55 Zero-Substitution Inception
Memorable Timestamps:
0:47 First Integral
2:30 Advanced U-Substitution
6:12 Integration by Parts (IBP)
7:28 Forced U-Substitution
10:24 IBP with Log & Zero-Substitution
11:53 Forced U-Sub over Expressing Tediously
13:29 Zero-Substitution!!!
16:56 Tricky Trig Integral
22:02 IBP with Inverse Function & Zero-Substitution
24:06 Super Sneaky U-Sub!!! (Remember this specific integral!!)
25:56 FULL-ON Forced U-Substitution
31:30 Last Integral (Advanced U-Substitution)
Memorable Timestamps:
00:14 First Integral (Reverse Product Rule)
1:34 Caveman Trick
4:39 IBP and Wallis Trick
8:03 Basic U-Sub
8:57 Trig Manipulation (Converting sines and cosines into tangents and secants)
11:43 Forced U-Sub
12:48 Radical Forced U-Sub
16:37 Simple U-Sub
17:46 Experiment with your derivative (Blind U-Sub)
20:51 Algebraic Conjugation
23:10 Integration by Parts & Zero Substitution
24:50 Awkward Exponentials
26:00 Basic U-Sub
26:44 Trigonometric Conjugation
28:07 Manipulate the Numerator (Zero-Substitution)
31:03 A Very Tricky Forced U-Sub + Geometric Polynomial Division
38:39 Symmetry
39:30 Another Tricky Forced U-Sub + Arctan with Constants
43:36 Basic U-Sub
45:30 Trig Manipulation (Converting tangents into sines and cosines)