Integration Strategy

Integration Strategy

1. Basic Substitution Method

   • Trigonometric Functions
     • Double-angle formula
     • Half-Angle formula
     • Trigonometric Identities
     • Addition formula
   • Inverse Trigonometric Functions
   • Hyperbolic Functions
   • Inverse Hyperbolic Functions
   • Natural Logarithm
   • Exponential Functions
   • General Exponential Functions

2. Completing the square

3. Trigonometric Identities

   • When to use trigonometric identities technique??
     • (a) when you have the summation of two terms power by two OR (b) when you have different angle

4. Improper Fraction

   • When to use improper fractions technique???
     • when you have improper fraction (degree of numerator> degree at denominator)

5. Separating Fractions

6. Multiplying by a Form of 1

   • Used to multiply the expression by some term divided by itself

7. Eliminating Square Roots

   • (a) When you have a trigonometric functions in the square root (b) the trigonometric functions can be simplified to a squared trigonometric form

8. Integration by Parts

   • How to choose u and dv??

9. Integration of Rational Functions by Partial Fractions

   • The rules of partial fractions 1) The numerator must be in lower degree than of the denominator 2) Factorize the denominator into its prime factor

10. Trigonometric Integrals

11. Trigonometric Substitutions

12. Improper Integrals

    • Upper limit
      • Lower Limit
        • Both Limit
          • Upper endpoint
            • Lower endpoint
            • Interior point

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