1_Integration

1_Integration

1. BASIC SUBSTITUTION METHOD

   • RUNNING CHAIN RULE
     • DEFINITE
       • F - D - (I+ LOWER & UPPER)
         • FIND "U" , THEN DIFFERENTIATE "U" , INTEGRATE BUT DON'T FORGET TO PUT LOWER AND UPPER LIMIT
     • INDEFINITE
       • F - D - (I THEN +C)
         • FIND "U", THEN DIFFERENTIATE "U", THEN INTEGRATE AND +C 
   • TRIGONOMETRIC F(X)
     • INDEFINITE
       • M - S -
         • MEMORIZE AL FORMULAS AND SIMPLIFY THE EQUATION
         • I IF CAN
           • INTEGRATE IF WE CAN INTEGRATE IT
         • IF CANNOT I . THEN F - D - I
           • IF CANNOT INTERGRATE , THEN , FIND U, DIIFF U AND  INTEGRATE U 
     • DEFINITE
       • M - S
         • MEMORIZE ALL FORMULAS AND SIMPLIFY THE EQUATION
         • I IF CAN
         • IF CANNOT I THEN F-D-I
           • IF CANNOT INTEGRATE, THE FIND U DIFFERENTIATE U INTEGRATE U
   • NATURAL LOGARITHM
   • EXPONENTIAL F(X)
     • IF LINEAR FX THEN I
       • I FOR INTEGRATE
     • IF NOT LINEAR FX
       • S-F-D-I
         • SIMPLIFY IT THEN IDENTIFY "U" -> DIFFERENTIATE "U" --> INTEGRATE IT IF NO UPPER OR LOWER LIMITS THEN PUT +C
   • GENERAL EXPONENTIAL F(X)
     • IF LINEAR FX THEN I
     • IF NOT LINEAR FX
       • S-F-D-I
         • SIMPLIFY IT --> FIND "U" --> DIFFERENTIATE "U" --> INTEGRATE "U" , IF NO UPPER OR LOWER LIMIT THEN +C
   • INVERSE TRIGONOMETRIC FUNCTIONS
     • M - S - F - D - I
       • MEMORIZE ALL FORMULAS --> SIMPLIFY IT --> FIND "U" --> DIFFERENTIATE "U" --> INTEGRATE 
   • HYPERBOLIC F(X)
     • M - S - F - D - I
       • MEMORIZE ALL FORMULAS --> SIMPLIFY IT --> FIND "U" --> DIFFERENTIATE "U" --> INTEGRATE 
   • INVERSE HYPERBOLIC F(X)
     • M - S - F - D- I
       • MEMORIZE ALL FORMULAS --> SIMPLIFY IT --> FIND "U" --> DIFFERENTIATE "U" --> INTEGRATE

2. COMPLETING THE SQUARE

3. TRIGONOMETRIC IDENTITIES

4. IMPROPER FRACTION

5. SEPARATNG FRACTION

6. Multiplying by a form of 1

7. Eliminating square roots

8. Integration by parts

9. TRIGONOMETRIC INTEGRALS

10. integration of rational fx by partial fraction

11. Trigonometric Substitutions

12. IMPROPER INTEGRALS