XI STRATEGIES

XI STRATEGIES

1. Basic Substitution

   • Use U, differentiate to get du, then integrate

2. Completing the Square

   • Basic Substitution is not working
   • Have quadratic function at denominator
     • 1) Function have 2 variable + 1 constant
     • 2) Function in square root
   • To get 1 variable & 1 constant

3. Separating Fractions

   • Fractions can be separated
   • Denominator have more than 1 variable

4. Improper Fraction

   • Used when degree (power of x) of numerator more than at denominator
   • Polynomials use long division method

5. Multiplying By A Form of 1

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

6. Eliminating Square Root

   • Used when have trigo function in square root
   • Used when trigo function can be simplified using trigo identities to a squared trigo function

7. Trigo Identities

8. Integration By Parts

   • Used ILATE RULE for U
   • Used when other method not working
   • Tabular Integration
     • Integral ALGEBRAIC . TRIGO dx
     • Integral ALGEBRAIC . EXPONENTIAL dx

9. Rational Func By Partial Fractions

   • HEAVISIDE COVER UP method can be use only for Non Repeated Linear Factors
   • For Non Repeated Linear Factors, Irreducible (cannot factorize) Quadratic Factors, Repeated Linear Factors, Improper Fractions
   • Can use for algebraic & transcendental functions

10. Trigonometric Integrals

11. Trigonometric Substitution

12. Improper Integrals

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