Integration Problem: Partial Fractions

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SUMMARY

The discussion centers on integrating the function \(\frac{10}{(x-1)(x^2-9)}\) using partial fractions. The user seeks clarification on notation, specifically the use of constants like B versus Bx in the decomposition. It is confirmed that a term like +0x can be added to the numerator to facilitate the separation of fractions. Additionally, the factorization of \(x^2-9\) into \((x-3)(x+3)\) is highlighted as essential for the integration process.

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  • Understanding of partial fraction decomposition
  • Familiarity with polynomial factorization
  • Basic knowledge of integration techniques
  • Experience with algebraic manipulation of rational functions
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  • Study the method of partial fraction decomposition in detail
  • Practice integrating rational functions with complex denominators
  • Explore the implications of different notations in partial fractions
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Students and educators in calculus, particularly those focusing on integration techniques and partial fraction decomposition. This discussion is beneficial for anyone looking to deepen their understanding of rational function integration.

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Homework Statement



[tex]\int[/tex]10/(x-1)(x^2-9)

Homework Equations


The Attempt at a Solution



I believe I should integrate by partial fractions here, but I'm not entirely sure on the notation. I've seen examples in my textbook that sometimes use B as opposed to Bx. Is this when that notation corresponds to a x^2?

Can this be done without having a factor of x in the numerator? If so would I just stick a +0x in the numerator before I separate?
 
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x2-9 can be factored as (x-3)(x+3)

if you had

[tex]\frac{1}{x-A)(ax^2+bx+c)}[/tex]

and b2-4ac<0 i.e no real roots then the fractions would be

[tex]\frac{F}{x-A}+\frac{Gx+H}{ax^2+bx+c}[/tex]
 

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