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Step-by-step Solution
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Divide $4x^3-2x^2+x+16$ by $x^2-2x+4$
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$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+4;}{\phantom{;}4x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}+4\overline{\smash{)}\phantom{;}4x^{3}-2x^{2}+x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+4;}\underline{-4x^{3}+8x^{2}-16x\phantom{;}\phantom{-;x^n}}\\\phantom{-4x^{3}+8x^{2}-16x\phantom{;};}\phantom{;}6x^{2}-15x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+4-;x^n;}\underline{-6x^{2}+12x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{;-6x^{2}+12x\phantom{;}-24\phantom{;}\phantom{;}-;x^n;}-3x\phantom{;}-8\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((4x^3-2x^2x+16)/(x^2-2x+4))dx. Divide 4x^3-2x^2+x+16 by x^2-2x+4. Resulting polynomial. Expand the integral \int\left(4x+6+\frac{-3x-8}{x^2-2x+4}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int4xdx results in: 2x^2.