Integration Strategies

Integration Strategies

1. Linear Functions

   • *0 Basic Rule

2. 2 different functions other than power 1

   • One is differential coefficient of the other
     • *1 Basic Substitution Method
       • (Certain functions need to be manipulated before substituting)
       • *see 0, 3-8, 10

3. Trigonometric Functions

   • *2 Trigonometric Identities
     • *see 1
   • *3 Integration
   • Inverse Trigonometric Functions
     • *7 Integration

4. Natural Logarithmic Functions

   • *4 Integration

5. Exponential Functions

   • *5 Integration

6. General Exponential Functions

   • *6 Integration

7. Hyperbolic Functions

   • *8 Integration
   • *9 Hyperbolic Identities
     • *see 1
   • Inverse Hyperbolic Functions
     • *10 Integration

8. Special Methods

   • Completing the Square
     • No substitutions available
     • Quadratic Functions
       • 3 terms (2 variables + 1 constant)
       • 2 terms (2 variables)
       • In square root
   • Trigonometric Identities
     • Summation of 2 terms power 2
     • Different angles
   • Long Division
     • Improper Functions
   • Separating Fractions
     • Two or more terms that share the same denominator
   • Eliminating Square Roots
     • Trigonometric function in square root
     • Trigonometric function can be simplified to a squared trigonometric
   • Multiplying by the Form of 1
     • Cannot be simplified by identities
   • Integration by Parts
     • When the 7 techniques do not work
     • Two functions where one is not a differential coefficitent of the other
     • Tabular Integration
       • Algebraic * Trigonometric
       • Algrbraic * Exponential
     • ILATE Rule
   • Integration of Rational Functions by Partial Fractions
     • Numerator is not the differential coefficient of the denominator
     • Heaviside Cover-up Method for non-repeated linear factors
     • Rules
   • Reduction Formula
     • Trigonometric function with high power
   • Trigonometric Substitution

9. Other Forms

   • Products of Powers of Sines and Cosines
   • Products of Sines and Cosines
   • Sums of Sines and Cosines at the Denominator
   • Sums of Squares of Sines and Cosines at the Denominator
   • Improper Integrals
     • Integrand Becomes Infinite
       • Separate into 2 integrals with limits approaching left and right sides of vertical asymptote
     • Infinite Limits of Integration
       • Separate into 2 integrals with limits approaching -/+ infinity
         • Range between 0 and -/+ infinity

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