Final answer to the problem
$x^{3}+2x^{2}-x$
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Step-by-step Solution
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- Write in simplest form
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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- Weierstrass Substitution
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1
Divide $x^5+12x^2-5x$ by $x^2-2x+5$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+5;}{\phantom{;}x^{3}+2x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}-2x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}+12x^{2}-5x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5;}\underline{-x^{5}+2x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+2x^{4}-5x^{3};}\phantom{;}2x^{4}-5x^{3}+12x^{2}-5x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5-;x^n;}\underline{-2x^{4}+4x^{3}-10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}+4x^{3}-10x^{2}-;x^n;}-x^{3}+2x^{2}-5x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+5-;x^n-;x^n;}\underline{\phantom{;}x^{3}-2x^{2}+5x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}x^{3}-2x^{2}+5x\phantom{;}-;x^n-;x^n;}\\\end{array}$
2
Resulting polynomial
$x^{3}+2x^{2}-x$
Final answer to the problem
$x^{3}+2x^{2}-x$
