Partial Fraction Expansion of



Partial Fraction Expansion
               
-1 
-1 
-2  -6 
24  -6  -6  24 
120  -24  12  -12  24  -120 
720  -120  48  -36  48  -120  720 
5040  -720  240  -144  144  -240  720  -5040 
40320  -5040  1440  -720  576  -720  1440  -5040  40320 




Note on Partial Fraction Decomposition

 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 tex2html_wrap_inline12974 , introduce terms

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For each factor of the form tex2html_wrap_inline12978 , introduce terms

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Then write

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and solve for the tex2html_wrap_inline12984 s and tex2html_wrap_inline12986 s.

References

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