1_INTEGRATION TECHNIQUES

1_INTEGRATION TECHNIQUES

1. Basic Substitution Method

2. Completing the Square

   • When?
     • Cannot use Substitution
     • Quad. fn at denominator
       • in square root
       • cannot factorize

3. Trigonometric Identities

   • When?
     • summation of 2 terms power two
     • different angle

4. Improper Integrals

5. Trigonometric Substitutions

6. Integration by Parts

   • either fn. is not the differential coefficient of other
     • How to identify?
       • ***
         • use ILATE
   • Tabular integration
     • • differentiate repeatedly until become zero
     • special case
       • • stop until get - sign

7. Separating Fractions

   • to get simpler integrand

8. Multiplying by form of 1

   • multiply the integrand by some term divided by itself

9. Eliminating Square Root

   • When?
     • trigonometric fn. in square root
     • trigo fn. can be simplify
       • HINT!! - use trigo identities -refer graph (check sign) -manipulate to get power 2

10. Trigonometric Integrals

    • Half - Angle Formulae
    • Reduction Formulae
    • products of powers of Sines and Cosines
    • substitution of t

11. Improper Fraction

    • How to solve?
      • use long division method

12. Integration of Rational Functions

    • by Partial Fraction
    • nonrepeated
    • repeated
    • irreducable quad. fn.
    • improper fraction
    • transcedental