INTEGRATION STRATEGY

INTEGRATION STRATEGY

1. Simplify Integrand

   • Algebraic Method
     • Basic Substitution Method
       • Trigonometric Function
         • Trigonometric Identities
           • Sum of 2 Terms of Power 2
             • Expansion
               • Multiplying by A Form of 1
                 • Natural Logarithm Function
                   • Solved
                 • Solved
           • Different Angle
             • Addition Formula
               • Separating Fraction
                 • Solved
                 • Inverse Trigonometric Function
                   • Solved
                 • Inverse Hyperbolic Function
                   • Solved
                 • Natural Logarithm Function
                   • Solved
         • Eliminating Square Root
           • Trigonometric Function In Square Root
             • Trigonometric Function
               • Natural Logarithm Function
                 • Solved
           • Trigonometric Function in Square Root (Can be Simplified)
             • Trigonometric Function
               • Natural Logarithm Function
                 • Solved
         • Trigonometric Integral
           • Reduction Formula
             • Solved
           • Powers of Sine and Cosine
             • Break into Squares and Power 1
               • Basic Substitution Method
                 • Solved
               • Trigonometric Identities
                 • Basic Substitution Method
                   • Solved
           • Product of Sine and Cosine
             • Sin(A)Cos(B)
               • (1/2)((Sin(A+B))+(Sin(A-B)))
                 • Solved
             • Sin(A)Sin(B)
               • (1/2)((Cos(A-B))-(Cos(A+B)))
                 • Solved
             • Cos(A)Cos(B)
               • (1/2)((Cos(A+B))+(Cos(A-B)))
                 • Solved
           • Integrals in Form ∫(1/(a+b((Sin x)^2)+c((Cos x)^2))
             • Basic Substitution Method (t=tan x)
               • Inverse Trigonometric Function (terms of (tan^-1))
                 • Solved
           • Integrals in Form ∫(1/(a+b(Sin x)+c(Cos x))
             • Basic Substitution Method (t=tan (x/2))
               • Inverse Trigonometric Function (terms of (tan^-1))
                 • Solved
           • Trigonometric Substitution
             • sqrt ((a^2)-(x^2))
               • x=asinθ OR x=acosθ
                 • Trigonometric Identities
                   • Solved
             • sqrt ((a^2)+(x^2))
               • x=atanθ
                 • Trigonometric Identities
                   • Solved
             • sqrt ((x^2)-(a^2))
               • x=asecθ
                 • Trigonometric Identities
                   • Solved
           • Products of Powers of Sine and Cosine
             • m is Odd
               • Trigonometric Identities
                 • Solved
             • m is Even and n is Odd
               • Trigonometric Identities
                 • Solved
             • Both m and n are Even
               • Trigonometric Identities (Half Angle Formulas)
                 • Solved
       • Natural Logarithm Function
       • Natural Exponential Function
       • General Exponential Function
       • Inverse Trigonometric Function
         • No factorisation
           • Completing The Square
             • Inverse Trigonometric Function
               • Basic Substitution Method
                 • Natural Logarithm Function
                   • Solved
             • Inverse Hyperbolic Function
               • Basic Substitution Method
                 • Natural Logarithm Function
                   • Solved
           • Improper Fraction
             • Long Division
               • Inverse Trigonometric Function
                 • Basic Substitution Method
                   • Natural Logarithm Function
                     • Solved
               • Inverse Hyperbolic Function
                 • Basic Substitution Method
                   • Natural Logarithm Function
                     • Solved
       • Hyperbolic Function
       • Inverse Hyperbolic Function
       • Other Methods
         • Integration by Parts
           • Convenient Definition of u and dv
             • Natural Logarithm Function
               • Collection of Repeated Terms
                 • Solved
               • Solved
             • Trigonometric Function
               • Collection of Repeated Terms
                 • Solved
               • Solved
         • Tabular Integration
           • Convenient Definition of u and dv
             • Solved
         • Rational Function
           • Partial Fractions
             • Non Repeated Linear Factors
               • Formula of (ax+b)
                 • Solved
             • Repeated Linear Factors
               • Formulas of (ax+b), ((ax+b)^2), ((ax+b)^3), (a(x^2)+bx+c)
                 • Solved
             • Irreducible Quadratic Factors
               • Formula of (a(x^2)+bx+c)
                 • Solved
             • Improper Fractions
               • Long Division
                 • Formulas of (ax+b), ((ax+b)^2), ((ax+b)^3), (a(x^2)+bx+c)
                   • Solved
             • Extension to Transcendental Functions
               • Basic Substitution Method
                 • Formulas of (ax+b), ((ax+b)^2), ((ax+b)^3), (a(x^2)+bx+c)
                   • Solved
         • Improper Integrals
           • Infinite Limits
             • Solved
           • Integrand Becomes Infinite
             • Solved