INTEGRATION

INTEGRATION

1. 1) Simplify & Identify

   • Simplify
     • Algebraic Manipulation
     • Trigonometic Identities
   • Identify Integrand
     • Product of COS & SIN?
     • Product of SEC & TAN?
       • Trigonometric
     • Product of CSC & COT?
     • Polynomial divided by Polynomial?
       • Partial Fraction
         • Non-repeating Linear
           • • use
               • Heaviside Cover Up
                 • • become
         • Repeating Linear
         • irreducible Quadratic

2. 2) Solving

   • a) Basic Substitution
     • "Let u"
   • b) If cannot
     • 1) Completing Square
     • 8) Separating Factors
     • 2) Eliminating Square Root
       • simplify then cancel out
     • 3) Improper Integral
       • Type I
         • Infinite Limits
       • Type II
         • Integrand Becomes Infinite
         • • x=a
           • x=b
           • x=c, a<c<b
           • Incontinuous at
     • 9) Integration By Parts
       • ILATE
         • i-inverse Trigo L-Log A-Algebric T-Trigo E-Exponential
       • Tabular Integration
     • 6) Long Division
     • 4) Trigonometric Identities
       • when
     • 7) Trigonometric Substitution
       • • If
     • 5) Multiply 1
       • Conjugation Method

3. 3) Try Again!

   • Trial & Error
   • Mix &Match Methods
   • Manipulate & Substitute

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