1_Solving Integration

1_Solving Integration

1. 2

   • Basic Substitution Method
     • Find u
       • u
         • has power
         • in √x
       • Differentiate u
         • Sub u and du into equation
     • If simple substituution doesn't work
       • Multiply form of 1
         • when
           • simplifying expression to expression that can be integrated
       • Improper Fraction
         • when
           • Degree numerator > degree denominator
       • Trigonometric Identities
         • when
           • Summation of 2 terms of power 2
           • Different angle
       • Completing The Square
         • when
           • Denominator of quadratic function
             • Cannot factorize
             • In √x
       • Separating Fraction
         • when
           • the fraction can be separated --> simpler integrand
       • Eliminating √x
         • when
           • have √trigo

2. 1

   • Simplify
     • Trigonometric Identities
     • Algebraic Manipulation

3. 3

   • Identify Integrand
     • Integration By Parts
       • when
         • poly X trigo
         • poly X expo
         • poly X log
       • use
         • ILATE
         • Tabular Integration
     • Partial Fraction
       • Have
         • Non-repeated Linear
           • Heaviside Cover Up Method
         • Repeated Linear
         • Irreducible Quadratic
       • when
         • Rational Expression
           • polynomial ÷ polynomial
     • Trigonometric Integral
       • when
         • product of sin & cos
     • Trigonometric Substitution
       • when
         • replace the variable of integration
     • Improper integral
       • when
         • Infinite limits of Integration
         • integrand becomes infinite

4. 4

   • Try Again
     • Try Substitution
     • Try parts
     • Manipiulate the integrand
     • Relate to previous problem
     • Use several methods

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