phinah 21 Aug 2018, 16:33
In decomposing the fraction of Chapter 11 Integration example 3 b, we are trying to figure out if there is a way to find the coefficients on `x^3` without expanding.
11. Integration By Partial Fractions
We expanded: `A(x^3 - x^2 - x - 1) +` ` ... +D(x^3 + x^2 + x- x^2 - x - 1)`
X
In decomposing the fraction of Chapter 11 Integration example 3 b, we are trying to figure out if there is a way to find the coefficients on `x^3` without expanding.
Relevant page <a href="https://www.intmath.com/methods-integration/11-integration-partial-fractions.php">11. Integration By Partial Fractions</a> What I've done so far We expanded: `A(x^3 - x^2 - x - 1) +` ` ... +D(x^3 + x^2 + x- x^2 - x - 1)`
Murray 22 Aug 2018, 02:29
I haven't heard of any other techniques for finding partial fractions outside of the one explained on the page you came from. (Paul's Online Notes does it the same way.)
I'm not quite sure what you are doing so far. What you have is equivalent to the following, and I'm not sure where it comes from:
`A(x^3 - x^2 - x - 1) + ... +D(x^3-1)`
X
I haven't heard of any other techniques for finding partial fractions outside of the one explained on the page you came from. (<a href="http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx">Paul's Online Notes</a> does it the same way.) I'm not quite sure what you are doing so far. What you have is equivalent to the following, and I'm not sure where it comes from: `A(x^3 - x^2 - x - 1) + ... +D(x^3-1)`
phinah 18 Apr 2019, 10:03
It was obtained by fully expanding `(x-1)^2(x-1)` = `x^3+x^2-2x^2-2x+x+1`. The same was done with `(x-1)^3.
But I now realize when seeking the coefficients for a term then only operate on that term. It is not necessary to fully expand and find the coefficient of each term if it is not needed.
X
It was obtained by fully expanding `(x-1)^2(x-1)` = `x^3+x^2-2x^2-2x+x+1`. The same was done with `(x-1)^3. But I now realize when seeking the coefficients for a term then only operate on that term. It is not necessary to fully expand and find the coefficient of each term if it is not needed.
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