Overview

Explore advanced calculus techniques in this comprehensive 7-hour video series on antidifferentiation. Master various integration methods including substitution, integration by parts, trigonometric integrals, trigonometric substitution, and partial fractions. Delve into hyperbolic functions, their properties, and applications. Learn L'Hôpital's Rule for evaluating limits and tackle improper integrals. Practice with numerous examples and gain a deep understanding of each concept through step-by-step explanations and problem-solving strategies.

Syllabus

Techniques of Integration: Substitution - 01. Intro.
Techniques of Integration: Substitution - 02. Definite integrals.
Techniques of Integration: Substitution - 03. Examples.
Techniques of Integration: Substitution - 04. Example.
Techniques of Integration: Substitution - 05. Examples.
Techniques of Integration - Substitution: 06. tan(x).
Techniques of Integration - Substitution: 07. sec(x).
Techniques of Integration - Substitution: 08. Trig Examples.
Techniques of Integration - Substitution: 09. Rational with Long Division.
Techniques of Integration - Substitution: 10. using arctan(x).
Techniques of Integration - Substitution: 11. Completing the Square.
Techniques of Integration - Substitution: 12. Requires Two Methods.
Techniques of Integration - Integration by Parts: 01. Introduction.
Techniques of Integration - Integration by Parts: 02. One Step Example.
Techniques of Integration - Integration by Parts: 03. Two Step Example.
Techniques of Integration - Integration by Parts: 04. Exponential times Cosine.
Techniques of Integration - Integration by Parts: 05. ln(x).
Techniques of Integration - Integration by Parts: 06. arctan(x).
Techniques of Integration - Integration by Parts: 07. Substitution, then parts.
Techniques of Integration - Integration by Parts: 08. Definite Integral.
Techniques of Integration - Trigonometric Integrals: 01. Introduction And Example.
Techniques of Integration - Trigonometric Integrals: 02. sin^5(x)cos^8(x).
Techniques of Integration - Trigonometric Integrals: 03. cos^4(x)sin^2(x).
Techniques of Integration - Trigonometric Integrals: 04. Product To Sum Identities.
Techniques of Integration - Trigonometric Integrals: 05. tan^2(x)sec^6(x).
Techniques of Integration - Trigonometric Integrals: 06. tan^3(x)sec^3(x).
Techniques of Integration - Trigonometric Integrals: 07. sec^3(x).
Techniques of Integration - Trigonometric Integrals: 08. A Reduction Formula.
Techniques of Integration - Trigonometric Integrals: 09. tan^6(x).
Techniques of Integration - Trigonometric Substitution: 01.Introduction.
Techniques of Integration - Trigonometric Substitution: 02. Sine Substitution.
Techniques of Integration - Trigonometric Substitution: 03. Tangent Substitution.
Techniques of Integration - Trigonometric Substitution: 04. Secant Substitution.
Techniques of Integration - Trigonometric Substitution: 05. Sine Substitution #2.
Techniques of Integration - Trigonometric Substitution: 06. Completing the Square.
Techniques of Integration - Trigonometric Substitution: 07. Tangent Substitution #2.
Techniques of Integration - Partial Fractions: 01. Introduction.
Techniques of Integration - Partial Fractions: 02. Decomposition Examples.
Techniques of Integration - Partial Fractions: 03. Finding Coefficients (solving systems).
Techniques of Integration - Partial Fractions: 04. Finding Coefficients (Heavyside method).
Techniques of Integration - Partial Fractions: 05. Repeated Linear Factor.
Techniques of Integration - Partial Fractions: 06. Alternate Technique for finding coefficients.
Techniques of Integration - Partial Fractions: 07. Need to Divide First.
Techniques of Integration - Partial Fractions: 08. Quadratic Factor - Setup.
Techniques of Integration - Partial Fractions: 09. Quadratic Factor - Integration.
Hyperbolic Functions: 01. Intro.
Hyperbolic Functions: 02. Graphs And First Properties.
Hyperbolic Functions: 03. Properties.
Hyperbolic Functions: 04. Derivatives And Integrals.
Hyperbolic Functions: 05. sinh(x) Inverse.
Hyperbolic Functions: 06. Hyperbolic Substitutions.
Hyperbolic Functions: 07. More Derivatives And Integrals.
Derivative Applications - L'Hosptital's Rule: 01. Introduction.
Derivative Applications - L'Hosptital's Rule: 02. Examples.
Derivative Applications - L'Hosptital's Rule: 03. Infinity over Infinity.
Derivative Applications - L'Hosptital's Rule: 04. Zero Times Infinity.
Derivative Applications - L'Hosptital's Rule: 05. Infinity Minus Infinity.
Derivative Applications - L'Hosptital's Rule: 06. Indeterminate Powers.
Techniques of Integration - Improper Integrals: 01. Introduction.
Techniques of Integration - Improper Integrals: 02. Examples.
Techniques of Integration - Improper Integrals: 03. With Integration By Parts.
Techniques of Integration - Improper Integrals: 04. Vertical Asymtotes.
Techniques of Integration - Improper Integrals: 05. The p-Test.
Techniques of Integration - Improper Integrals: 06. Direct Comparison.
Techniques of Integration - Improper Integrals: 07. Limit Comparison.