Integration Technique

Integration Technique

1. 1. Simplification

2. 2. Basic substitution method

3. 3. Completing the square

   • quadratic func can't factorise
     • 2v+1c
       • 2v

4. 4. Trigo identities

5. 5. Improper fraction

   • degree nume ≥ degree deno
   • long division

6. 6. Separating fractions

   • fractions separated
     • simpler integrand

7. 7. Multiply by form of 1

   • conjugation

8. 8. Eliminate square root

   • trigo in square root
     • trigo func simplified to squared trigo

9. 9. integration by parts

   • ILATE
     • ∫u dv
   • Tabular integration
     • ∫u dv
       • differentiate u until =0
   • Special Tabular integration
     • ∫u dv
       • differentiate u until get initial func

10. 10. ∫ of Rational func by partial fractions

    • a. non- repeated linear factors
    • heaviside cover up
    • b. repeated linear factors
    • c. irreducible quadratic factors
    • d. improper fraction
    • e. transcedental func

11. 11. Trigonometric Integrals

    • products of sines and cosines
    • • Method is to subs t=tan x

12. 12. Trigo substitution

13. 13. Improper Integral

    • type 1
    • type 2

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