Utilizing the Hermite-Ostrogradski Formula for the Integration of Rational Functions

The purpose of this report is to provide a clear and detailed presentation of the formula for the integration of rational functions known as the Hermite-Ostrogradski method. The proof of the formula will be given and applied to examples, demonstrating how this method of integration can prove superior to traditional method in certain situations. Also, the implementation of the formula utilizing computer algebra systems will be discussed as well as an additional method for hand computation The significance of this lies in the fact that it will unearth a largely forgotten result and will provide the reader with a more efficient method to integrate a large class of functions. A theoretical result and its proof is also included that permits one to recognize a large class of rational functions that can not be integrated in closed form