Techniques of Integration

Techniques of Integration

1. Double Substitution

   • This method of integration is implemented by using the generalized Power Rule
     • • And in the next example we can see how we can solve it using the generalized Power rule

2. Integration By Parts

   • This is my personal favorite way to integrate and the way it works is that you use the next formula
     • • To solve using this formula you need to identify your u and dv and to know this you need to know that u is always going to be the first in LATE (Logarithmic, Algebraic, Trigonometric, Exponential) and then you just find the derivate of u and the integral of dv and follow the formula to get to the answer

3. Partial Fractions

   • Proper Fraction
     • For the proper fraction its a little more complicated, what you need to do is to factor your what is down in the fraction, then you have to assign a letter, either A or B and put each part of your factorized equation below the A or B, then you need to assign values to your x to make them cancel each other out so in the end you have the values for the A and the B and in the end you just integrate.
   • Improper Fraction
     • For improper fraction it is really easy, you just have to do a long division to get to your answer, including the residue

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