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Mathematical Operations

Integration by Parts

Partial Fractions

Integration by Parts

Integration by parts is a technique for performing integration by expanding the differential of a product of functions and expressing the original integral in terms of a known integral .

A simple example illustrates the method of Integration by parts.
The requirement is to integrate the product x.cos(x)dx

Partial Fractions..Partial fractions are also covered on webpage laplace Transform -partial fraction

A complicated algebraic fraction can often be reduced to to its equivalent partial fractions such that it allows an integration process to be simplified.    A typical example is shown below

Rules for Partial fractions

A simple example of the application of these rules is as follows

The equations are solved for A and B as follows

A second example is provide below

Partial Fractions -Cover up rule

There are many simple cases where the cover up method can be used . This method only applies if the denominator of the original fraction has non-repeated , linear factors. The method is illustrated by the following example.

Useful Related Links
  1. Platonic Realms ...Very Extensive Mathematics Information /formulae.
  2. The Maths Pages.. Easy to follow mathematics notes.
  3. Scienceworld.wolfram .... Welcome to the best resource of Science and math on the Internet - Probably true
  4. Karls Calculus Tutor .... This is an excellent site for learning Calculus

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Last Updated 01/05/2010