1_1_2_1_Integration Strategy

1_1_2_1_Integration Strategy

1. 1. Memorise the formula

   • TRIGO & INVERSE
   • NATURAL LOG
   • HYPERBOLIC & INVERSE

2. 2. Simplify

   • TRIGO IDENTITIES
   • QUADRATIC
     • COMPLETING SQUAURE
       • a = 1, +ve
     • FACTORISE
   • SEPARATING FRACTION
     • **DENOMINATOR CAN'T BE SEPARATED

3. 3. "U"-Substitution

   • DIFFERENTIATE & ELIMINATE

4. 4. Identify the integral

   • RATIONAL FN
     • PARTIAL FRACTION
       • REPEATED LINEAR FACTOR
       • DISTINCT LINEAR FACTOR
         • Heaviside "cover up" method
       • IRREDUCIBLE QUADRATIC EQUATION
         • x factorise
       • IMPROPER FRACTION
   • FN IS NOT DIFFERENTIAL TO EACH OTHER
     • INTEGRATION BY PARTS
       • ILATE
       • TABULAR INTEGRATION (+ - + -)
         • ALGEBRAIC + TRIGO
         • ALGEBRAIC + EXPO
         • EXPO + TRIGO
   • VARIABLE CAN BE REPLACE BY TRIGO FN
     • TRIGO SUBSTITUTION
   • 1+TRIGO
     • MULTIPLY BY FORM OF 1
   • TRIGO FN IN SQUARE ROOT
     • ELIMINATING THE SQUARE ROOT
       • USE TRIGO IDENTITIES, **ABSOLUTE
   • POWER OF NUMEREATOR >= DENOMINATOR
     • IMPROPER FRACTION
       • LONG DIVISION
   • POWER OF TRIGO > 2
     • TRIGO INTEGRALS
       • REDUCTION FORMULA
       • PRODUCTS OF POWERS OF SIN AND COS
         • M = ODD
         • M = EVEN, N = ODD
         • M, N = EVEN
       • TRIGO IN DENOMINATOR
         • POWER OF TRIGO = 1
           • t = TAN X
         • POWER OF TRIGO = 2
           • t = TAN x/2
   • ∞ => ∞, ∞ => 0, 0 => -∞
     • IMPROPER INTEGRALS

5. 5. Multiple(maybe)

6. 6. Try again!

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