INTEGRATION STRATEGIES

INTEGRATION STRATEGIES

1. INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

2. TRIGONOMETRIC SUBSTITUTION

   • X = a tan θ X = a sin θ X = a sec θ

3. SEPARATING FRACTIONS

   • IF FRACTION CAN BE SEPARATED AND WILL RESULT TO SIMPLER INTEGRAND

4. ELIMINATING SQUARE ROOTS

   • WHEN YOU HAVE A TRIGONOMETRIC FUNCTION IN THE SQUARE ROOT
   • SIMPLIFY TO A SQUARED TRIGONOMETRIC FORM SO THE SQUARE ROOT CAN BE ELIMINATED

5. COMPLETING THE SQUARE

   • WHEN NO SUBSTITUTION AVAILABLE
   • WHEN YOU HAVE QUADRATIC FUNCTION AT DENOMINATOR
     • QUADRATIC FUNCTION CANNOT BE FACTORISE
     • QUADRATIC FUNCTION IS IN THE SQUARE ROOT

6. INTEGRATION BY PARTS

   • ILATE RULES
     • INVERSE TRIGO, LOGARITHMIC, ALGEBRAIC, TRIGONOMETRIC, EXPONENTIAL

7. IMPROPER FRACTION

   • WHEN YOU HAVE IMPROPER FRACTION
     • POWER AT NUMERATOR ≥ POWER AT DENOMINATOR

8. MULTIPLYING BY A FORM OF 1

   • MULTIPLY THE EXPRESSION BY SOME TERM DIVIDED BY ITSELF

9. TRIGONOMETRIC INTEGRALS

   • INTEGRATE FUNCTION TO THE POWER OF 2, USING HALF ANGLE FORMULA

10. TRIGONOMETRIC IDENTITIES

    • WHEN YOU HAVE THE SUMMATION OF THE TWO TERMS POWER TWO
    • WHEN YOU HAVE DIFFERENT ANGLE

11. IMPROPER INTEGRALS

    • UPPER LIMIT LOWER LIMIT BOTH LIMITS UPPER ENDPOINT LOWER ENDPOINT INTERIOR ENDPOINT

12. BASIC SUBSTITUTION

    • RUNNING THE CHAIN RULE BACKWARDS

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