partial fractions

The method of partial fractions is a technique used to integrate rational functions by expressing them as the sum of simpler rational expressions. This method relies on the fact that any rational function can be decomposed into a polynomial plus terms of specific forms, which can then be integrated individually.

Conditions and Properties

This decomposition is possible because any polynomial can be factored into linear and irreducible quadratic components, allowing the rational function to be represented as a sum of terms with denominators of these factored forms.

Applications

The method of partial fractions is primarily applied in the integration of rational functions, where it serves as a systematic approach to decompose complex fractions into simpler components.

Notes & references