Integration Techniques

Integration Techniques

1. Double Substitution

   • This method simplifies algebraically the form of a function in a way that its antiderivative is required. It is also known as u-substitution. It can be related differentially to the chain rule.

2. Partial Fractions

   • This method is used when the problem is an improper fraction (degree is higher on the numerator than the denominator). Long division will take place to simplify the problem. The division shall give a polynomial as well as a rational expression. This rational expression will be decomposed into partial fractions. Once a proper fraction has been achieved, the denominator will be factored by using quadratic or linear factors.

3. Tabular Method

   • This method uses a three column table. The first column represents "Signs" (either positive or negative), the second column represents "u", and the third column "dv". The order of the first column (signs) will always start with positive, then negative, and so on and so forth. The second columns brings the function that wants to be integrated all the way to 0 by differentiation. As for the final column, it will contain the repetitive action of integrating the problem. You then multiply the results on the table diagonally in order to get the final answer.

4. Integration by Parts

   • Integration by parts uses the following formula:
     • This method of integration requires to find the function "u" and the differential "dv". In order to detect these two on the equation, LATE must be used. L (Logarithmic), A (Algebraic), T (Trigonometric), and E (Exponential). The order of letter priority must be followed in order to detect "u" and "dv".

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