Memorable Timestamps:
0:37 - Factoring Further in Roots
1:35 - Utilizing U-Sub
6:00 - Absorbing Exponent Law
7:41 - Absorbed U-Sub
10:44 - Multiplying Functions Top and Bottom
16:45 - Exponential Absorbed U-Sub
19:27 - x^(3/2)=xsqrt(x) Mindset
22:39 - Getting Used to Cluttered Exponentials
23:59 - Hidden x^(3/2)
26:15 - Negative Exponents
29:40 - Advanced Absorbed U-Sub Case
31:38 - A Hidden Squared Binomial (Factoring Further in Roots)
Memorable Timestamps:
0:05 - Factoring Polynomials
1:51 - Don't Overcomplicate!
4:31 - Rational Factoring
7:01 - Synthetic Division
10:10 - Dividing top and bottom by a Function
12:08 - Conjugation
15:53 - Logarithm Law (Influencing the Exponent)
18:12 - Logatithm Law (Simplifying it Out)
20:51 - Don't Overcomplicate! (Completing the Square)
23:33 - A Secret Algebraic U-Sub!
27:53 - An Awkward Zero-Substitution
32:30 - A Harder Awkward Zero-Substitution
Memorable Timestamps:
1:08 Intro to Hyperbolic Trig
4:03 A Surprising Simple e^x
5:09 tanh(x) U-sub
5:51 Conjugating with Hyperbolic Trig
8:03 IBP with Hyperbolic Trig
8:35 A Simple Hyperbolic Trig Identity
9:37 Trig-Integration Approach
13:09 Multi-Sub with Sinh(2x)
13:57 tanh^2(x)+sech^2(x)=1
14:24 Exponential Looking Integral
16:53 Symmetry with Hyperbolic Trig
18:19 Another IBP with Hyperbolic Trig
19:03 Recursive IBP with Hyperbolic Trig
20:08 A Simple U-Sub
20:25 A Misleading Identity
21:31 Reverse Product Rule!!
22:20 A Hybrid of Hyperbolics!!
23:00 A Hidden Arctan Integral
Memorable Timestamps:
0:34 The Purpose of Converting
1:23 When We Can't Conjugate
4:08 Dodging IBP
4:54 Dodging Trig Identites
5:56 Dodging IBP to Foiling
7:30 Algebraic Factoring
8:58 A Forced Exponential Integral
11:28 An Uncomfortable Radical Exponential Integral
16:11 Hyperbolics with Infinities???
16:43 Pulling Out the Pascal Triangle
19:02 A Disguised Trig-Sub
21:18 Coolest & Sneakiest Absorbed U-Sub
25:05 A Very Uncomfortable Negative Exponential Integral
29:17 An Awkward Log Integral
33:11 An Intimidating U-Sub Integral
36:10 A Stacking Exponential Integral
37:30 Another Hidden Arctan Integral
Memorable Timestamps:
0:28 The Purpose of Hyperbolic Trig-Sub
4:38 Converting a Radical into Exponentials
10:26 Introducing Inverse Hyperbolic Trig
13:38 More Radicals into Exponentials
22:23 A Weird tanh Integral
24:30 An Awkward IBP
27:40 Ugliness to Simple IBP
Memorable Timestamps:
0:18 Basic Inverse Trig Identity
2:44 A Tricky Inverse Trig Identity for [0, pi/2]
4:34 Complex Inverse Trig Identity (Using the Triangle)
6:36 THEY'RE JUST CONSTANTS!!!
9:43 A Hidden Absolute Function
11:36 Utilizing the Constants Algebraically
14:46 A Hidden Constant Function
17:49 My Sneakiest Favorite Integral
Memorable Timestamps:
1:46 Concept Integral
3:18 Applying Loophole Log Trick
7:34 U-Substitution Type
9:11 Devouring a Monster Integral
11:51 Improper Integral Example
17:24 Experimenting with U-Subs
21:47 MIT Style Integral Example
Memorable Timestamp:
0:48 The Basics of Manipulation
3:21 Multiplying Top and Bottom by a Trig Function
6:24 Converting sinx & cosx into secx & tanx
12:09 A Constant Changes Everything
20:21 Using Complex Algebra to Check our Identities
27:02 Using System of Equations to Purposely make 2 Easy Integrals
36:40 Another Constant that Changes Everything
40:46 Identity Manipulating
44:18 Periodic Manipulation
50:55 Another Another Constant that Changes Everything
53:22 A Chain of Tangents
57:22 A Chain of Sines
1:01:23 Sneakiest Trinomial Conjugation
Memorable Timestamp:
0:19 Getting rid of the Radical
1:48 Force Subbing
3:49 Power Sub the Cube Root!!
6:25 Dealing with Relatively Prime Radical Roots
10:09 Avoiding Fractional Power Rule
11:45 More Power Sub with Cube Roots
12:46 More Relatively Prime Radical Roots
16:39 MIT Integration Bee Example
20:50 Don't Conjugate!!
23:37 A Messy Power Substitution
27:14 A Terrible Disgusting Example
Memorable Timestamps:
0:29 Concept
4:18 A Common Example
6:59 Experimenting with Derivatives
11:58 Undertowing more than One Functions
17:08 A Sneaky Negative Attack
19:54 More Mixtures of x and e^x
21:28 Last Integral
Memorable Timestamps:
0:49 Logarithmic Substitution
2:32 Inverse U-Substitution
4:05 Avoid Overcomplicating
6:24 Radical U-Substitution
11:10 Take the Whole Denominator
15:32 Dealing with Exponential Functions
16:59 More Logarithmic Substitution
18:57 Lambert W Function Example
25:32 Norwegian Substitution
28:39 Blind Substitution
31:41 British Substitution
36:38 More Sneaky Forced U-Subs
38:05 Triggy British Substitution
Memorable Timestamps:
0:47 A Beginner Review
1:13 The Common e^x Trick
2:53 Quotient Rule Example
7:21 Revealing the Product Rule with U-Sub
8:24 More Practice on Quotient Rule
10:07 Dealing with Radicals
12:13 An Advanced Example for Finding f(x)
16:21 Reciprocal Functions Example
20:39 Famous Monstrous JEE Main Example
Memorable Timestamps:
0:22 Beginner Concept
3:34 Choosing which Term to IBP
4:56 Double Semi-IBP
8:07 A Triggy Semi-IBP
10:38 Another simple Semi-IBP
12:00 Another Double Semi-IBP
14:02 Switching Terms for Better Semi-IBP
15:38 More Easy Semi-IBP
16:36 Sneaky tan(x/2) Example
20:39 Double Semi-IBP with Reciprocals
Memorable Timestamps:
0:35 A Common Textbook Decisive IBP
5:53 Recycle the Integral with Decisive IBP
11:20 A Very Common Integration Bee Problem
12:35 Arctan with Logs
16:49 A Nightmarish Integral with Arcsech(x)
19:56 MIT Style Integral
21:12 DON'T OVERDO IT!! A Secret U-Sub Trick.
Memorable Timestamp:
0:25 - Concept Explanation
2:07 - Beginner Example
3:02 - A Realistic Example
5:52 - Completing the Square Example
7:44 - A Hidden Case
10:14 - JEE Main Example - Splitting to 2 Variants Case
15:15 - A Sneaky Modified Substitution
Memorable Timestamp:
0:34 - Square-Square Concept
3:26 - A Beginner Example
8:12 - A Spivak Example
12:17 - Dodging Nasty Partial Fractions
13:35 - A Trig-Sub Example
16:17 - A Difficult Splitting Case
22:18 - Another Splitting Case
24:48 - A Dangerous Improper Bound Case
Memorable Timestamp:
0:21 - A Beginner Example
2:57 - Getting Rid of the Inverse Trig
6:01 - Chebyshev Polynomial???
12:00 - An Iterating Trig-Sub Integral!!
17:56 - Remember the Purpose of Trig-Subbing!!
20:20 - Famous Indian Trig-Sub Monster!!
26:01 - More Definite Integrals
33:09 - Remember our Sin(2x)+1 Trick?
Memorable Timestamp:
0:32 - The Concept
2:40 - Beginner Examples
4:47 - Advanced Examples
7:00 - Just a lil trig manipulation
7:54 - A Forced U-Sub Example
10:53 - A Hyperbolic Surprise!!!
Memorable Timestamp:
0:37 The Formula Concept
1:14 A Beginner Example
1:54 A Logarithmic Example
3:36 Rewrite the Bounds
4:29 Substitution Example
5:20 Spam the Factorial Formula
8:06 A Radical Example
8:40 A Power Sub Example
9:50 More U-Sub Examples
11:13 A Very Tricky Example from HMMT
13:27 A Weird U-Sub Example
14:04 A Hyperbolic Trig-Sub Example
Memorable Timestamp:
0:10 Gamma Function Concept
1:34 Beta Function Concept
9:39 Easy Beta Example
12:12 Trig Beta Example
14:43 Tricky Formula Beta Example
17:02 U-Sub Example
18:14 Square Root Example
20:25 Dealing with Big Numbers
21:32 Famous Golden Ratio Example!!
31:11 Exponential Example
32:13 Don't Overdo it!!
35:06 Radical Beta Example
Memorable Timestamps:
0:18 Gaussian Formula Concept
1:24 Basic Common Gaussian Integral
2:38 Using Symmetry
3:44 Intro to Dealing with Annoying Constants
4:36 Utilizing Loophole Log
6:36 Completing the Square
7:39 Square Root U-Sub
8:37 A Trig Example
9:51 A Log Example
11:23 A Beautiful Log Example
12:56 A Caution U-Sub Example
14:54 This Converges???
17:23 A RADICAL Looking Gaussian Integral
18:31 Remembering the Log Form
21:30 An Awkward Gaussian in Disguise
22:36 A Hyperbolic Trig Example
24:36 A Cool Loophole Log Example
Memorable Timestamps:
0:19 Concept Formula
2:44 First Example / Sneaky U-Sub
3:36 Trig Identity Example
4:32 A Deceiving Example
11:28 A Nicer IBP Example
12:13 Don't Be Intimidated
12:56 Using Half Angle Identity
13:45 Sneaky Exponential Sub
14:22 An Odd Dirichlet Integral
15:09 Just a Reverse Quotient Rule Conjoined
16:41 A Very Sneaky Advanced U-Sub