Strategy for Integration

Strategy for Integration

1. 1. Simplify Integrand

   • Addition formula
   • Double angle formula
   • Half angle formulas
   • Phytagorean Identities
   • Reciprocal Identities

2. 4. Manipulate Integral

   • using trigonometric identities
     • have summation of 2 terms power two
     • have different angle
   • completing the square
     • no substitution can be done
     • quadratic function at denominator
       • quadratic function in square root
       • quadratic function cannot be factorized
   • using improper function techniques
     • degree of numerator > degree of denominator
     • use long division method
   • eliminating square roots
     • have trigonometric function in square root

3. 2. Simple Substitution

   • let u
     • inside bracket
     • under the
     • denominator

4. 3. Classify Integrand

   • Trigonometric function
     • use substitution
   • Rational function
     • use partial fractions
       • factorize denominator into its prime factors
       • must be in proper fractions
   • Radicals
     • use trigonometric substitution
     • use rationalizing substitution
   • Trigonometric function Exponential function Logarithmic function
     • use Integration by parts

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