I need to get $$\frac{x^4-2x^2+4x+1}{x^3-x^2-x+1} $$ into a specific form for integration. I have factored out my denominator to $(x-1)^2(x+1)$ through grouping. I am unsure how to use polynomial division to divide this because of the factored denominator and I have divided it by the unfactored denominator and arrived with a remainder which didn't help at all with the integration process.
2026-04-23 06:21:16.1776925276
Help getting this integral into specific form for integration.(Polynomial Division)
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The polynomial long division gives $$ x^4-2x^2+4x+1=(x^3-x^2-x+1)(x+1)+4x $$ so your fraction is $$ \frac{x^4-2x^2+4x+1}{x^3-x^2-x+1}=x+1+\frac{4x}{x^3-x^2-x+1} =x+1+\frac{4x}{(x-1)^2(x+1)} $$ Now you can find the partial fraction decomposition $$ \frac{4x}{(x-1)^2(x+1)}= \frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C}{x+1} $$