INTEGRATION STRATEGY

INTEGRATION STRATEGY

1. SIMPLIFY INTERGRAND

   • ALGEBRA
     • FACTORISATION
     • EXPANSION
   • TRIGONOMETRIC IDENTITIES

2. USE SUBSTITUTION

   • LET u = g(x)
     • CALCULATE du
       • SUB BOTH ACCORDING TO EQUATION FORM
         • INTERGRATE ACCORDINGLY

3. RECOGNIZE FORMULA

   • BASIC
   • EXPONENTIAL
   • GENERAL EXPONENTIAL
   • TRIGONOMETRY
   • INVERSE TRIGNOMETRY
   • HYPERBOLIC FUNCTION
   • INVERSE HYPERBOLIC FUNCTION
   • LOGARITHM

4. CLASSIFICATION

   • TRIGONOMETRIC
     • USE SUBSTITUTION if
       • f(x) IS PRODUCT OF TRIGONOMETRY FUNCTION
   • RATIONAL
     • USE PARTIAL FRACTION
   • RADICALS
   • BY PARTS
     • • PRECEDENCE
   • IMPROPER INTERGRAL
     • TYPE 1: INFINITE LIMITS OF INTERGRATION
     • TYPE II: INTERGRAND BECOMES INFINITE

5. MANIPULATE INTEGRAND

   • ELIMINATE SQUARE ROOTS
     • SIMPLIFY TO A SQUARED TRIGONOMETRIC FORM SO THAT THE SQUARE ROOT CAN BE ELIMINATED
   • COMPLETING THE SQUARE
     • WHEN NO SUBSTITUTIONS ARE AVAILABLE
     • WHEN YOU HAVE QUADRATIC FUNCTION AS THE DENOMINATOR
       • QUADRATIC FUNCTION CANNOT BE FACTORIZED
       • QUADRATIC FUNCTION IS IN A SQUARED ROOT
   • MULTIPLYING BY A FORM OF ONE
     • A/B X A/A
   • PARTIAL FRATION

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