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YT 4 minutes 29 seconds
Eddie Woo
Integrating Rational Polynomials (Example)
YT 3 minutes 41 seconds
Eddie Woo
Partial Fractions (example with cubic denominator)
YT 7 minutes 23 seconds
Eddie Woo
Partial Fractions for Integrating Rational Polynomials
YT 6 minutes 20 seconds
Eddie Woo
Partial Fractions w/ Perfect Square Denominators
YT 3 minutes 59 seconds
Eddie Woo
Rearranging Rational Polynomials w/ Division Transformation
YT 6 minutes 20 seconds
Eddie Woo
Deriving Integration by Parts
YT 8 minutes 23 seconds
Eddie Woo
Integration by Parts - Example 1: x cos x
YT 2 minutes 46 seconds
Eddie Woo
Integration by Parts - Example 2: x*e^x & x²*e^x
YT 2 minutes 11 seconds
Eddie Woo
Integration by Parts - Example 3: ln x
YT 5 minutes 11 seconds
Eddie Woo
Integration by Parts - Example 4: e^x * sin x
YT 8 minutes 1 second
Eddie Woo
An unusual integral with two very different solutions?
YT 7 minutes 42 seconds
Eddie Woo
Integration by Parts - Example 5: sin¯¹(x)
YT 7 minutes 10 seconds
Eddie Woo
Integrals that lead to Logarithmic Functions
YT 14 minutes 54 seconds
Eddie Woo
Introduction to Recurrence Relations
YT 12 minutes 31 seconds
Eddie Woo
Recurrence Relation Example: Integrating (sin x)^n
YT 4 minutes 33 seconds
Eddie Woo
Recurrence Relations without IBP (1 of 2): (tan x)^n
YT 3 minutes 27 seconds
Eddie Woo
Recurrence Relations without IBP (2 of 2): (x^n)/(x+1)
YT 5 minutes 2 seconds
Eddie Woo
Sometimes integration by parts is a bad idea...
YT 3 minutes 51 seconds
Eddie Woo
Integrating with t-results (1 of 3): Example integral through identities
YT 9 minutes 57 seconds
Eddie Woo
Integrating with t-results (2 of 3): Changing the variable of integration
YT 5 minutes 24 seconds
Eddie Woo
Integrating with t-results (3 of 3): Further example
YT 5 minutes 9 seconds
Eddie Woo
Why do logarithmic functions have absolute value signs after integration?
YT 9 minutes 5 seconds
Eddie Woo
Integrating √[x/(1-x)] by Trigonometric Substitution
YT 3 minutes 51 seconds
Eddie Woo
Correction of Wrong Solution from Fitzpatrick (integration question)
YT 14 minutes 27 seconds
Eddie Woo
Tricky Recurrence Relation with Unexpected Algebraic Manipulation
YT 12 minutes 6 seconds
Eddie Woo
Evaluating Recurrence Relations
YT 11 minutes 49 seconds
Eddie Woo
Proving Properties of Definite Integrals (1 of 2)
YT 3 minutes 26 seconds
Eddie Woo
Proving Properties of Definite Integrals (2 of 2)
YT 8 minutes 56 seconds
Eddie Woo
3 Definite Integrals Evaluated by Trigonometric Substitution
YT 6 minutes 9 seconds
Eddie Woo
Integrating √(16-x²)/x² by Trigonometric Substitution
YT 4 minutes 19 seconds
Eddie Woo
Integrating √[(1+x)/(1-x)] by Trigonometric Substitution
YT 11 minutes 59 seconds
Eddie Woo
Evaluating Definite Integral w/ t-results
YT 8 minutes 34 seconds
Eddie Woo
Integral of sin(x)tan²(x): Three Approaches
YT 5 minutes 26 seconds
Eddie Woo
Proving Inequality from an Increasing Function
YT 3 minutes 59 seconds
Eddie Woo
Proving Inequality from Prior Integral
YT 5 minutes 53 seconds
Eddie Woo
Proving that a function is increasing
YT 7 minutes 55 seconds
Eddie Woo
Using Properties of Definite Integrals: Trigonometric Integrand (1 of 2)
YT 7 minutes 29 seconds
Eddie Woo
Determining Algebraic Recurrence Relation
YT 9 minutes 9 seconds
Eddie Woo
Expressing I(n) without Recursion
YT 5 minutes 25 seconds
Eddie Woo
Using Properties of Definite Integrals: Trigonometric Integrand (2 of 2)
YT 7 minutes 57 seconds
Eddie Woo
Harder (Ext 2) Integral Requiring Substitution
YT 8 minutes 13 seconds
Eddie Woo
Harder (Ext 2) Integral Question (1 of 2: Manipulating the Recurrence Relation)
YT 10 minutes 9 seconds
Eddie Woo
Harder (Ext 2) Integral Question (2 of 2: Evaluating Related Limiting Sum)
YT 13 minutes 47 seconds
Eddie Woo
Partial Fractions (1 of 3: Introducing an identity to simplify a quadratic denominator)
YT 5 minutes 5 seconds
Eddie Woo
Partial Fractions (2 of 3: An alternative method to find introduced variables)
YT 11 minutes 59 seconds
Eddie Woo
Partial Fractions (3 of 3: How to use Partial Fractions to split fractions with Quadratic Numerator)
YT 10 minutes 45 seconds
Eddie Woo
Partial Fractions: Quadratic Factors (1 of 2: Issues with non-linear denominator factors)
YT 6 minutes 37 seconds
Eddie Woo
Partial Fractions: Quadratic Factors (2 of 2: Problems with Quadratic Factors and Solution)
YT 9 minutes 41 seconds
Eddie Woo
Partial Fraction: Repeated Linear Factors (Technique for Breaking down into partial fractions)
YT 14 minutes 14 seconds
Eddie Woo
Integration of Square Root Function (1 of 2: Using a Trig Substitution to help with integration)
YT 9 minutes 12 seconds
Eddie Woo
Integration of Square Root Function (2 of 2: What is this kind of integral solving for?)
YT 5 minutes 48 seconds
Eddie Woo
Further Integration (1 of 2: Brief Overview of Extension II Integration)
YT 8 minutes 38 seconds
Eddie Woo
Further Integration (2 of 2: Integrating Trig Functions without given substitution)
YT 10 minutes 49 seconds
Eddie Woo
Further Integration [Continued] (1 of 3: Using Double Angle & Completing the Square to integrate)
YT 6 minutes 17 seconds
Eddie Woo
Further Integration [Continued] (2 of 3: Adding and subtracting a constant to simplify integral)
YT 4 minutes 49 seconds
Eddie Woo
Further Integration [Continued] (3 of 3: 'Breaking Apart' Integrals to simplify for integration)
YT 6 minutes 8 seconds
Eddie Woo
Partial Fractions & Integration (Using Partial Fractions to simplify an integral for evaluation)
YT 7 minutes 20 seconds
Eddie Woo
Harder Reverse Chain Rule Integral (Using a Substitution and Restrictions to evaluate)
YT 8 minutes 14 seconds
Eddie Woo
Proving a Result from the Standard Integrals (1 of 3: Differentiate, Hence Integrate Proof)
YT 7 minutes 23 seconds
Eddie Woo
Proving a Result from the Standard Integrals (2 of 3: Substituting tan to simplify the integral)
YT 11 minutes 28 seconds
Eddie Woo
Proving a Result from the Standard Integrals (3 of 3: Using Partial Fractions to simplify sec)
YT 10 minutes 49 seconds
Eddie Woo
Integration with t-results (1 of 2: Changing the variable of integration)
YT 7 minutes 42 seconds
Eddie Woo
Integration with t-results (2 of 2: Dealing with the integral in t)
YT 5 minutes 5 seconds
Eddie Woo
Integration by Parts (1 of 3: Deriving the Formula)
YT 8 minutes 14 seconds
Eddie Woo
Integration by Parts (2 of 3: How to choose u & dv)
YT 9 minutes 39 seconds
Eddie Woo
Integration by Parts (3 of 3: Integral of sin¯¹(x))
YT 4 minutes 24 seconds
Eddie Woo
Integration by t results (Explanation of Harder Question)
YT 7 minutes 44 seconds
Eddie Woo
Integration by Parts (What to choose for u and dv for integration by parts?)
YT 6 minutes 16 seconds
Eddie Woo
Integration with t Results (1 of 2: Changing the variable to solve with t results)
YT 7 minutes 47 seconds
Eddie Woo
Integration with t Results (2 of 2: Simplifying the integral before applying t results)
YT 7 minutes 58 seconds
Eddie Woo
Recurrence Relations (1 of 4: Introduction to Recurrence relations with introductory examples)
YT 10 minutes 23 seconds
Eddie Woo
Recurrence Relations (2 of 4: Considering if the question consists of some arbitrary power of n)
YT 11 minutes 19 seconds
Eddie Woo
Recurrence Relations (3 of 4: Applying to Trigonometric Functions raised to power of n)
YT 4 minutes 49 seconds
Eddie Woo
Recurrence Relations (4 of 4: Integration by parts with definite integrals)
YT 5 minutes 30 seconds
Eddie Woo
Evaluating Recurrence Relations (1 of 4: When do you apply Recurrence Relations?)
YT 9 minutes 11 seconds
Eddie Woo
Evaluating Recurrence Relations (2 of 4: Using Integration of parts to build recurring pattern)
YT 6 minutes 48 seconds
Eddie Woo
Evaluating Recurrence Relations (3 of 4: Using Recurring Pattern to group Relation in a series)
YT 10 minutes 9 seconds
Eddie Woo
Evaluating Recurrence Relations (4 of 4: Finding a term free of integrals)
YT 8 minutes 18 seconds
Eddie Woo
Extension 2 Exam Review (1 of 7: Integration by Substitution, Partial Fractions)
YT 8 minutes 23 seconds
Eddie Woo
Extension 2 Exam Review (2 of 7: Recurrence Relation, Graph Transformations)
YT 9 minutes 31 seconds
Eddie Woo
Mathematics Extension 1 Exam Review (1 of 3: Integration by substitution)
YT 9 minutes 49 seconds
Eddie Woo
Integration by Parts (2 of 2: When the integrand doesn't look like a product)
YT 10 minutes 42 seconds
Eddie Woo
Integration by Parts (1 of 2: Arranging the integral with DETAIL)
YT 7 minutes 13 seconds
Eddie Woo
Integration with Quadratic Denominators (3 of 3: Rationalising the numerator)
YT 14 minutes 20 seconds
Eddie Woo
Integration with Quadratic Denominators (2 of 3: Distinguishing characteristics)
YT 10 minutes 24 seconds
Eddie Woo
Integration with Quadratic Denominators (1 of 3: Introduction - why are they challenging?)
YT 12 minutes 48 seconds
Eddie Woo
Partial Fractions (3 of 3: Three solution methods)
YT 9 minutes 4 seconds
Eddie Woo
Partial Fractions (2 of 3: What are they?)
YT 7 minutes 51 seconds
Eddie Woo
Partial Fractions (1 of 3: Review questions)
YT 14 minutes 47 seconds
Eddie Woo
Integration by Unspecified Substitution (3 of 3: Trigonometric example)
YT 13 minutes 16 seconds
Eddie Woo
Integration by Unspecified Substitution (2 of 3: Square root example)
YT 8 minutes 42 seconds
Eddie Woo
Integration by Unspecified Substitution (1 of 3: Introductory example)
YT 12 minutes 50 seconds
Eddie Woo
Intro to Further Integration (2 of 2: Foundational examples)
YT 16 minutes 49 seconds
Eddie Woo
Intro to Further Integration (1 of 2: Expanding on prior learning)
YT 16 minutes 44 seconds
Eddie Woo
Recurrence Relations (3 of 3: Trigonometric examples)
YT 7 minutes 56 seconds
Eddie Woo
Recurrence Relations (2 of 3: Exponential example)
YT 11 minutes 38 seconds
Eddie Woo
Recurrence Relations (1 of 3: Introduction & logarithmic example)
YT 8 minutes 50 seconds
Eddie Woo
Recurrence Relation - worked example (1 of 2: Integration by parts)
YT 7 minutes 57 seconds
Eddie Woo
Recurrence Relation - worked example (2 of 2: Connecting the integrals)
YT 15 minutes 11 seconds
Eddie Woo
Logarithmic integral with recurrence relation (Exam Question 4 of 10)
YT 11 minutes 31 seconds
Eddie Woo
Integral via partial fractions (Exam Question 9 of 10)
YT 9 minutes 11 seconds
Eddie Woo
Reverse chain rule integral (Exam Question 7 of 10)
YT 8 minutes 12 seconds
Eddie Woo
Recurrence Relation (1 of 6: Setting up integration by parts)
YT 10 minutes
Eddie Woo
Recurrence Relation (2 of 6: Relating consecutive integrals)
YT 9 minutes 21 seconds
Eddie Woo
Recurrence Relation (3 of 6: Establishing the pattern)
YT 13 minutes 24 seconds
Eddie Woo
Integrating sec⁸θ
YT 12 minutes 58 seconds
Eddie Woo
Inequality proof from integration by parts
YT 9 minutes 26 seconds
Eddie Woo
Recurrence Relation (4 of 6: Expressing without integrals)
YT 13 minutes 32 seconds
Eddie Woo
Recurrence Relation (5 of 6: Trigonometric substitution)
YT 12 minutes 42 seconds
Eddie Woo
Recurrence Relation (6 of 6: Proving an inequality)
YT 18 minutes 51 seconds
Eddie Woo
Integration: how to choose boundaries with trigonometric substitution
YT 10 minutes 19 seconds
Eddie Woo
Integration by substitution (two ways)