Strategy Of Integration

Strategy Of Integration

1. 1. Simplify

   • Use Trigonometric Identities or Algebraic manipulation
   • To know the method that can be used

2. 2. Substitution

   • Find function u=g(x) in the integrand whose differential du=g'(x)dx also occur

3. 3. Classify

   • Trigonometric Function (TF)
     • Use Substitution if f(x) is a product of powers of TF
   • Rational Functions
     • Use partial fractions if 'f' is a rational function
   • Integration By Parts
     • Only if f(x) is a product of a power of x and a transcendental function
   • Radicals
     • When ppppppppp , use trigonometric substitution
     • When ppppp, use rationalizing substitution ppppppp, Sometimes it work on pppp

4. 4. Retry

   • 1. Try Substitution
     • 2. Try parts
       • 3. Manipulate The Integrand
         • 4. Relate The Problem With The Previous Problems
           • 5. Use Several Methods
           • Use a method on a given integral that is similar to a method used in the previous integral
         • Algebraic manipulations (Rationalizing the denominator or using trigonometric identities)

5. Formulas

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