Integration Strategy :)

Integration Strategy :)

1. 1. Simplify the equation to the simplest form !

2. BASIC SUBSTITUTION METHOD

   • 1. Identify 'u'
   • 2. Differentiate 'u ' to get 'du'
   • 3. Substitute 'u' and 'du' into original equation and solve

3. 3. MANIPULATE

   • a. Separating the fraction
     • 1. Separate the integrals by separating fracion
     • 2. Use substitution method / trigonometric identities
     • 3. Solve
   • b. Multiplying by the form of one
     • 1. Multiply the expression by form of one
     • 2. Use substitution method / trigonometric identities
     • 3. Simplify by separating fraction
     • 4. Solve
   • c. Eliminating square roots
     • 1. Simplify the trigonometric functions to squared trigonometric function
     • 2. Eliminate the square root.
     • 3. Look for any obvious substitution
     • 4. Classify integrals according to its form
     • 5. Solve
   • d. Completing the square
     • 1. Simplify by completing square
     • 2. Use basic substitution method
     • Solve

4. Trigonometric / Hyperbolic Formula

5. 4. IDENTIFY THE TYPE OF INTEGRAL

   • Improper Integral
     • Use limit
       • Infinite Limits of Integration
         • Upper limit
         • Lower limit
         • Both limits
       • Integrand becomes limit
         • Upper endpoint
         • Lower endpoint
         • Interior point
   • Rational Expressions (polynomial/polynomial)
     • Use partial fractions
       • Linear factor (ax+b)
       • Factor (ax+b)^2
       • Quadratic Factor (ax^2+bx+c)
       • Factor (ax+b)^3
   • Integration by Parts
     • • • I. Inverse Trigo/Inverse Hyperbolic 2.Logarithmic/General Logarithmic 3.Algebraic 4.Trigo/Hyperbolic 5.Exponential/General Exponential
       • Tabular Integration
         • Only applied for integration of: 1.algebraic x trigo 2. algebraic x exponential
   • Trigonometric Integral
     • • Use Half-Angle Formulas
     • • Separate to get two terms
     • Reduction Formula
     • Product of cosine and sine
       • • 1. When 'm' is odd 2. When 'n' is odd 3. When 'm' and 'n' is even
       • • Use Trigonometric Identities
     • Substitution-t method
       • • t= tan x/2
       • • t=tan x
   • Trigonometric Substitution

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