Integration Strategy

Integration Strategy

1. Manipulate

   • when you cannot integrate directly, use
     • form of 1
     • manipulation of power
     • identities
     • conversion of log into ln

2. substitute, usually for these types of functions, (which dy/dx, y exist in the function)

   • hyperbolic
     • use derivatives
   • general exponential
     • use (a^u)/lna
   • natural log
     • use f(x) / f'(x)
   • power function, indicated by
     • bracket
     • root
     • denominator
   • trigo function
     • use identities
     • use derivatives
   • exponential
     • when u = linear
       • use (e^u)/(du/dx)
   • inverse trigo
     • memorize 3 formulas
   • inverse hyperbolic
     • memorize 5 formulas
   • trigo substitution
     • substitute variable x with
       • a tan(theta)
       • a sec(theta)
       • a sin(theta)

3. clasiffy

   • type of function
     • quadratic function cannot be factorize
     • quadratic function in square root
       • use CTS
     • improper fraction
       • use long division method
     • trigo function in square root
       • eliminate the root by manipulating function to power 2
     • rational function which has 3 types of factors
       • non repeated linear factors
         • Know the 6 rules and HEAVISIDE cover method
       • repeated linear factors
       • inreducible quadratic factors
     • trigo function with power
       • use addition,half angle or reduction formula
       • if another form, which is 1 over trigo function with power
         • subs t=tanx
   • multiplication of 2 different functions
     • usually, use either
       • integration by parts
       • tabular integration
         • NOTE: There is special case!

4. simplify, by using either

   • factorization
   • expansion, if
     • or summation of 2 term, power 2
       • then use trigo identities
     • different angles
   • separation of fractions

5. try again, by using

   • multiple technique, which is
     • the combination of several out of 11 techniques