Abstract: A usual method is the method of waiting coefficient to solve integral of a rationalfunction. We shall propose a non-waiting coefficient formula of solution about thiskind of integral in this article and perfectly solve this kind of integral problem. Inpractical application this new method is simple, direct and effective. Its advantage isnot only to give a simple solution for several problems which are very difficult or aren'tsolved by usual method, but also to solve more complex problems by computer.

Key words: expansion of a polynomial, rational function, integral of rationalfunction