INTEGRATION STRATEGY

INTEGRATION STRATEGY

1. Multiplying by Form of 1

   • Plus/Minus at the Denominator (CONJUGATED)
   • Simplify expression that can be Integrated

2. Completing the Square

   • Quadratic at Denominator (INVERSE TRIGONOMETRIC)

3. Eliminating Square Root

   • Trigonometric Identities
     • Addition Formula
     • Pythagorean Formula
   • Squaring inside --> LOSE SQUARE ROOT

4. Improper Fraction

   • Long-Division

5. Separating Fraction

   • Add/Minus at Numerator

6. Partial Fraction Method

   • Linear Factor
     • x have power
     • Can factorise
   • Repeated Linear Factor
     • Bracket have power
   • Irreducible Quadratic Factors
     • x have power
     • Cannot Factorise

7. Product

   • Integration by Parts
     • • u --> easy to Differentiate dv/dx --> easy to Integrate
   • Tabular Integration

8. Improper Integral

   • Type I
   • Type II

9. Trigonometric Identities

   • Pythagorean
   • Addition
   • Double-Angle
   • Half-Angle

10. Trigonometric Integrals

    • Half-Angle
      • Power of sin/cos > one
    • Reduction Formula
    • • ODD Number (Separate)
      • EVEN Number (Half-Angle Formula)
    • • Addition Formula
    • • tan x = t
    • • tan x/2 = t

11. Trigonometric Substitutions

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