Integration Techniques

Integration Techniques

1. Change of Variable/ Double Substitutiom

   • Apply substitution for "u"
     • Solve for "dx"
       • Input the values of "u" and "dx" in the equation
         • Leave everything in terms of "u"
           • Simplify and multiply
             • Then just integrate

2. Partial Fractions

   • Factor the denominator of the equation
     • Use capital letters (A,B,C,..) to separate the factors into fractions, the factor as a denominator and the capital letter as nominator
       • Multiply everything by the factors
         • Rearrange the equation
           • Solve for the capital letters, one letter at the time.
             • To solve for one letter, input a value to cancel the other letters
               • Once you have the values of the letters, input the values in the equation
                 • Finally just integrate

3. Integration by Parts

   • When we can't cancel any variable we use the integration by parts
     • To know the "u" in the equation we use the Nemotechnique rule
       • Nemotechnique rule= LATE= L (Logarithmic) A (Algebraic) T (Trigonometric) E (Exponential)
         • General rule for integration by parts
           • How to integrate
             • Find "du"
               • Find "dv"
                 • Then input the values of "u" and "dv" in the equation for integrate
                   • And finally integrate and simplify
     • Tabulation method
       • Sometimes running the integration by parts process only once will not be enough to solve the integral and we will have to run the process several times
         • In some cases we can use a table as a shortcut of using the process more than once

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