Basic Integration

• Integrating basic polynomial terms
• Some integration properties
• Integrating basic rational functions
• Extra solved problems from rational and polynomial combinations

• Integrating terms with square roots
• Integrating terms with rational functions extended
• Integrating basic exponential functions
• Integrating trigonometric functions
• Integrating trigonometric functions part II
• Special tricks we can use in integration
• Definite integration

Integration By Substitution

• Why we need integration by substitution?
• Chain rule Vs Integration by substitution
• How to know whether to use integration by substitution or not?
• Integration by substitution problem solved slowly, step by step
• More easy examples
• Medium level examples
• More medium level examples
• Hard examples
• More hard examples

Integration By Parts

• Integration by parts formula explanation
• How to use formula correctly?
• How to use formula correctly - more examples
• LIATE Rule
• Special examples
• Integration by parts twice
• Never ending integration by parts
• Examples where LIATE doesn't work
• More hard examples
• When to use integration by substitution or parts?

Trigonometric Integration

• Why/When we use Pythagorean identity
• Why/When we use double angle identity
• Integrating trigonometric functions with only even power
• Integrating trigonometric functions with only even power more examples
• Integrating trigonometric functions with odd power
• Integrating trigonometric functions with odd power examples
• Integrating trigonometric functions with tangent and secant functions
• Integrating trigonometric functions with tangent and secant functions more examples

Trigonometric Substitution

• Trigonometric Substitution Preparation-How to simplify the square root
• Trigonometric Substitution- Substitutes and their use
• Trigonometric Substitution-Example-1
• Converting the solution back to original from from theta
• Trigonometric Substitution-Example-2
• Trigonometric Substitution-Example-3
• Trigonometric Substitution-Example-4
• Trigonometric Substitution-Example-5
• Trigonometric Substitution-Example-6
• Trigonometric Substitution-Example-7
• Trigonometric Substitution-Example-8
• Completing the square review
• Trig Substitution and completing the square-Example-9
• Trig Substitution and completing the square-Example-10

Partial Fraction Decomposition

• What is really PFD?
• Different cases based on different types of rational functions
• Linear distinct factors
• Repeated linear factors
• Irreducible factors
• Examples-1
• Evaluating constants
• Examples-2
• Case-2-Larger numerator
• Examples-3
• Examples-4
• Integration-Linear distinct factors
• Integration-Repeated linear factors
• Integration-Irreducible factors
• Examples-5
• Examples-6
• Examples-7
• Case-2-Examples-8
• Examples-9

Approximate Integration

• Why we need approximate integration?
• What is definite integral?
• Riemann Sum - review
• Left end point rule
• Left end point rule example
• Right end point rule
• Overestimation Vs Underestimation
• Midpoint rule
• Trapezoidal rule
• Simpson's rule formula derivation
• Error bound formula-1
• Error bound formula example
• Finding K in the error bound formula I
• Finding K in the error bound formula II
• Error bound example 2
• Error bound example 3

Improper Integrals

• Type I improper integrals
• Type II improper Integrals
• Exercise for classifying improper integrals as type I and II
• What is convergence & divergence of an improper integral?
• Basic example of a solving type I improper integral
• Solved examples - Type I improper integrals -1
• Solved examples - Type I improper integrals -2
• Solving type II improper integrals -1
• Solving type II improper integrals -2‍
• Solving type II improper integrals-3
  
  
  
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