Integration Strategy.

Integration Strategy.

1. Basic substitution method (using Let U / changing of variables)

   • Indefinite Integral & Definite Integral
     • Trigonometric
       • Using derivatives
       • Using identities
       • • Using substitution
     • Natural Logarithmic
       • Using Derivatives
     • Exponential
       • Using derivatives
     • General Exponential
     • Inverse Trigonometric
       • Using Derivatives
     • Hyperbolic
       • Using derivatives
     • Inverse Hyperbolic
       • Using derivatives
     • Polynomials
       • How to substitute?
         • Pick integrand with root
         • Pick integrand with bracket
         • Pick the denominator integrand

2. Classify functions

   • Functions with distinguished characteristics
     • Trigo function in square root
       • eliminate the square root by using trigonometric identities
     • Improper fraction
       • use long division method
     • Quadratic function is in the square root
       • Use completing the square
     • Trigo function with power
       • Function with power of 2
         • Substitute with half angle and addition formula
       • Function with power > 2
         • Use reduction and addition formula (identities)
           • For sin
           • For cos
       • Reciprocal of trigo function (use t substitution)
         • trigo function with power of two
           • t = tan x
         • trigo function with power of one
           • t = tan x/2
     • Quadratic function can't be factorized
       • Use completing the square
     • Rational functions (know & apply all 6 rules of partial fractions)
       • non-repeated linear factor
         • Use Heaviside Cover Up Method
       • repeated linear factors
       • irreducible quadratic factors
   • Product of two functions using :
     • Integration by parts
       • Using ILATE
     • Tabular
       • Differentiate the variable until it becomes 0
         • special case when tabular is not applicable, integrate by using the formula until a part of the question is obtained and can be equated with the question

3. When function can't be integrated directly

   • Convert log to ln
   • Use identities
   • Manipulate the power
   • Simplify the function , by :
     • Factorization
     • Separation of fraction
     • expansion, if
       • different angles exist
         • Use trigo identities
       • Summation of two terms with the power of 2
   • If can't be solved with one technique
     • Use combination of several techniques

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