So far, we have seen how to evaluate integrals in which the integrand is of the

form 1/(ax/b) or 1/(ax2/bx/c). These are special cases of an integrand of the form


D(x) ,

in which N (x ) and D (x ) are both arbitrary polynomials. Such expressions

are called rational functions of x . To evaluate the integral of a general rational


g N(x)D(x) dx, it is necessary to decompose N (x )/D (x ) into a sum of simple rational functions

to which, if the degree of N (x ) equals or exceeds the degree of D (x ), there must

be added a polynomial. Each term resulting from such a decomposition can

then be integrated by one of the techniques discussed so far. This process of

decomposition is called expressing N (x )/D (x ) in terms of partial fractions.