INTEGRATION

INTEGRATION

1. STEP 1:SIMPLIFY

   • TRIGO IDENTITY
   • HYPERBOLIC IDENTITY
   • SEPARATING FRACTION
   • MULTIPLY BY A FORM OF 1
   • ELIMINATING SQUARE ROOT
   • TRIGO INTEGRAL
     • High power of sinx and cos x
       • reduction formula

2. STEP 2: SIMPLE SUBSTITUTION

   • FIND U
     • dU/dx
       • substitute

3. STEP 3:SIMPLE SUBSTITUTION DO NOT WORK

   • quadratic function at denominator
     • COMPLETING THE SQUARE
   • cannot factorize
   • ʃ ( _ +_ )² dx
   • different angle
     • TRIGONO IDENTITIES
   • numerator >denominator
     • IMPROPER FRACTION
   • Polynomial x trigo func/ exponential/logarithm
     • INTEGRATION BY PARTS
   • numerator not differential coefficient of the denominator
     • PARTIAL FRACTION
   • • TRIGONOMETRIC SUBSTITUTION
   • TYPE 1: INFINITE LIMITS OF INTEGRATION
     • IMPROPER INTEGRAL
   • TYPE 2 : INTEGRAND BECOME INFINITE

4. STEP 4: TRY AGAIN !

   • if the earlier technique does not work

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