Partial Fraction Expansion | |||||||||
---|---|---|---|---|---|---|---|---|---|

0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

1 | 1 | ||||||||

2 | 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 2 | -1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 |

4 | 6 | -2 | 2 | -6 | 0 | 0 | 0 | 0 | 0 |

5 | 24 | -6 | 4 | -6 | 24 | 0 | 0 | 0 | 0 |

6 | 120 | -24 | 12 | -12 | 24 | -120 | 0 | 0 | 0 |

7 | 720 | -120 | 48 | -36 | 48 | -120 | 720 | 0 | 0 |

8 | 5040 | -720 | 240 | -144 | 144 | -240 | 720 | -5040 | 0 |

9 | 40320 | -5040 | 1440 | -720 | 576 | -720 | 1440 | -5040 | 40320 |

A Rational Function *P*(*x*)/*Q*(*x*) can
be rewritten using what is known as partial fraction decomposition. This
procedure often allows integration to be performed on each term separately
by inspection. For each factor of *Q*(*x*) the form
, introduce terms

For each factor of the form , introduce terms

Then write

and solve for the s and s.

**References**

Beyer, W. H. *CRC
Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press,
pp. 13-15, 1987.