Integration Game Plan

Integration Game Plan

1. Substitution

   • Indefinite integral
     • • Tactic: expand term by term
         • make sure power x any number except -1
       • • For linear function only!!
   • Definite integral
     • Tactic:be careful with upper and lower limits
       • when variable changes,upper and lower limit change
         • last variable for final answer follow original given
   • Trigonometric function
   • Natural logarithmic
     • • Tactic:follow properties of logarithmic
         • factorize to find best u
           • ln1=0;based on graph
   • Exponential function
     • • Tactic:priority u is power of e
         • must simplify function until achieve form of e^u only integrate
   • General exponential function
     • • Tactic:when x is variable, integrate using GEF
   • Inverse trigonometric function
     • • Tactic:make sure a is 1 only continue integrating function
         • Stewart's table
   • Hyperbolic function
     • • Tactic:integrate as usual
   • Inverse hyperbolic function
     • • Tactic:be careful with range of limit for each integral

2. Completing the square

   • Example
     • Tactic:1.use when subs. inconvenient
       • 2.when quadratic function(QF) at denominator
         • 3. QF cannot factorize/in square root

3. Trigonometric identities

   • • Tactic:1.must expand the function first
       • 2.use when trigonometric function power two
         • 3.use when exist different angle

4. Improper fractions

   • Tactic:1.use when numerator bigger than or equal to denominator
     • 2.change improper fraction into proper fraction

5. Separating fractions

   • Tactic:1.apply when numerator has more than 1 term
     • 2.separate fraction when its proper function&subs. inconvenient

6. Multiplying by a form of 1

   • Tactic:apply conjugation technique

7. Eliminating square roots

   • Tactic:1.use when trigo in square root
     • 2.trigo can be converted to smtg power two so can cancel out with square root

8. Integration by parts

   • • Tactic:1.use when all techniques learn previously unavailable
   • Tabular integration

9. Partial Fractions

   • 1.only for proper fraction 2.when substitution method is unavailable 3. always factorize the function first if possible 4.use long division to change into proper fraction if initial function is improper
     • • A,B and C must be real numbers

10. Trigonometric Integrals

    • Reduction formula
      • • x of sin & cos
          • • Identities
              • • sub t=tan x

11. Trigonometric substitution

12. Improper integral

    • type 1
      • • type 2

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