Integration by Partial Fractions: Example 1

in mathematics •  4 months ago  (edited)

In this video I go over an example on using the method of partial fractions for integrating rational functions. In this example I go over the integral of (x3+x)/(x-1) and break it down using polynomial long division. The remainder partial fraction is simple enough to integrate so we do not need to go any further in breaking it down using partial fraction decomposition.


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Integration of Rational Functions by Partial Fractions: Example 1

Integration by Partial Fractions Example 1.jpeg

Example:

Solution:

Since the degree of the numerator is greater than the degree of the denominator the rational function is improper so we can first perform polynomial long division:

Note:

In this example we only needed to perform polynomial long division and not break the remainder into further partial fractions because we were able to solve the integral easily.

In later examples I will show how we need to apply the techniques in partial fraction decomposition to enable us to solve the integral.

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