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Partial Fraction Integration - Set up problems?

by demersal
Tags: fraction, integration, partial
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Sep22-08, 09:38 PM
P: 41
1. The problem statement, all variables and given/known data
[tex]\int[/tex][tex]\frac{2x^{2}}{(x^{2}-1)}[/tex] dx

2. Relevant equations
Partial Fractions

3. The attempt at a solution
2[tex]\int[/tex][tex]\frac{x^{2}}{(x^{2}-1)}[/tex] dx

2[tex]\int[/tex][tex]\frac{x^{2}}{(x-1)(x+1)}[/tex] dx

[tex]\frac{A}{x-1}[/tex] + [tex]\frac{B}{x+1}[/tex] = [tex]\frac{x^{2}}{(x+1)(x-1)}[/tex]

A(x+1) + B(x-1) = x[tex]^{2}[/tex]

Solving for coefficients does not work because there is no x[tex]^{2}[/tex] term of A or B and also when solving for the x and the constant contradictory answers occur. Did I set this up wrong??
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Sep22-08, 10:31 PM
PF Gold
P: 1,131
Perhaps try polynomial long divison first
Sep22-08, 11:19 PM
P: 41
I can't believe I didn't see that; thank you!!

Sep22-08, 11:34 PM
PF Gold
P: 1,131
Partial Fraction Integration - Set up problems?

No problem

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