Integration Strategies

Integration Strategies

1. Basic Substitution Method

   • • 1. Identify 'u'
       • u = 1+x^3
     • 2. Differentiate 'u' to get 'du'
       • du = 3x^2
     • 3. Substitute 'u' and 'du' into original question and solve

2. Completing The Square

   • • 1. Simplify by completing the square
     • 2. Use basic substitution method
       • u = x+2 du=1dx
     • 3. SOLVE

3. Improper Fraction (when degree of denominator is smaller or same as degree of numerator)

   • • 1. Use long division method
     • 2. Rearrange the equation from step 1
     • 3. Solve ( basic substitution method is used if necessary)

4. Separating The Fraction

   • • 1. Simplify (separate) the integrals by separating the fraction
     • 2. Use substitution method / trigonometric identities based on question
     • 3. Solve

5. Multiplying by form of one

   • • 1. Multiply the expression by the form of one
     • 2. Use substitution method / trigonometric identities based on queation
     • 3. Simplify by separating the fraction
     • 4. Solve

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