STRATEGY FOR INTEGRATION

STRATEGY FOR INTEGRATION

1. STEP 1

   • SIMPLIFY
     • Trigonometric Identities
       • • Basic Identities
       • Addition Formula
       • Half- Angle Formula
       • Double-Angle Formula

2. STEP 2

   • SUBSTITUTION
     • Look for obvious, simple substitution
       • • Substitution method is used instead of partial fractions
     • Choose 'u' that can eliminate the original integral after differentiate

3. STEP 3

   • IDENTIFICATION OF INTEGRAL
     • Trigonometric Function
       • Involve integral product of powers
     • Rational Function
       • Use partial fraction when a polynomial is divided by a polynomial
     • Polynomial and Transcendental
       • Trigonometry Exponential Logarithm
         • Use integration by parts
           • By using formula
     • Quadratic Function
       • Use completing the square
     • Radicals
       • Use trigonometric substitution
       • Use rationalizing substitution

4. STEP 4

   • TRY AGAIN
     • Try substitution
     • Use several methods
       • * Several successive substitutions of different types * Combine integration by parts with one or more substitutions
     • Try parts
       • * Use integration by parts * Effective on single and inverse functions
     • Manipulate the integrand
     • Relate the problem to previous problems
       • • NOTE : If it has been evaluated, the calculation can be used in the next problem

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