INTEGRATION TECHNIQUES

INTEGRATION TECHNIQUES

1. Double Substitution

   • Double substitution works when you got a function that has double terms and cannot be canceled by one another
     • Step 1: Get your "u" and "du" in order to get your "x" and "dx"
       • Step 2: After you've got all your terms, then we just need to substitute them with "u" and "x"
         • Step 3: At the end just solve the integral with the "Generalized Power Rule"

2. Partial Fractions

   • Partial Fractions method can be used on integrals that its denominator can be factorized
     • Step 1: In order to get your main equation, you need to cancel some terms through distributive property
       • Step 2: So now that you've got your main equation, then you must find your "A", "B" and "C" depending in how many terms you need to find.
         • Step 3: At the end we just substitute the values you found into your inicial equation and just integrate with the logarithmic rule or generalized power rule depending on the case

3. Integration by parts

   • Integration by parts can be used on functions that have double terms and cannot be canceled by one another, Also this terms must be: Logarithmic, Algebraic, Trigonometric or Exponential
     • Step 1: We need to identify which term is gonna be our "u" with LATE (Logarithmic, Algebraic, Trigonometric or Exponential) in that order. Then the rest of the equation is going to be your dv and just get your du by derivating "u" and your "v" by integrating your "dv"
       • • Step 3: Just integrate to get your final answer
         • However in such cases that we need to use integration by parts method several times, then:

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