INTEGRATION STRATEGY

INTEGRATION STRATEGY

1. Need to know the formulas!

   • Exponential Function
   • General exponential function
   • Trigonometric function
   • Natural Logarithmic
   • Inverse trigo
   • Hyperbolic function
   • Inverse hyperbolic

2. Simplify the integrand if possible

   • Algebraic Manipulation
   • Trigonometric identities
     • Basic identities
     • Double angle
     • Half angle
     • Addition formula

3. Try again!

   • Try substitution
     • (if not work out) Try parts
       • Single function
       • Manipulate the integrand
         • Relate the problem to previous one
           • Use several methods
             • Successive subs
             • Integration by Parts + subs
         • Rationalizing the denominator
         • Trigo identities

4. Look for obvious subs

   • U = g(x)
     • dU = g'(x)

5. Classify the integral based on its form

   • Partial fraction
     • Quadratic factor
     • Non-repeated linear factor
     • Repeated linear factor
     • Irreducible quadratic factor
   • Polynomial x exponential, logarithmic and trigonometric function
     • Integration by parts (ILATE)
   • Products of trigonometric functions
   • Quadratic
   • Radicals

Imagens e arquivos do mapa