Partial fraction (math-1) tutorial

Key Concepts

Partial Fraction Decomposition of a Rational Function

• If the rational function is improper, use "long division" of polynomials to write it as the sum of a polynomial and a proper rational function "remainder."
  
  
• Decompose the proper rational function as a sum of rational functions of the form
  A(x−)kandBx+C(x2+x+)k(x2+x+ irreducible)
  where:
  • Each factor (x−)m in the denominator of the proper rational function suggests terms
    A1(x−)+A2(x−)2++Am(x−)m
  • Each factor (x2+x+)n suggests terms
    B1x+C1(x2+x+)+B2x+C2(x2+x+)2++Bnx+Cn(x2+x+)n
• Determine the (unique) values of all the constants involved.
  
  
  • Use either Method 1 or Method 2, or a combination of both.

The partial fraction decomposition is often used to rewrite a complicated rational function integrand as a sum of terms, each of which is straightforward to integrate.

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