Rational Function

A rational function is a quotient of two polynomials,

Using the Quotient, Constant, Sum, and Power Rules, one can easily find the derivative of any rational function. We shall now show how to find the integral of any rational function. This is fairly easy to do if the degree of the denominator G(x) is only two or three, but becomes more difficult as the degree of G(x) gets larger. Let us work some examples and then formulate a general procedure.

Our first example shows how to integrate when the denominator G(x) has degree one.

Example 1