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Divide $x^4-6x^3+12x^2+6$ by $x^3-6x^2+12x-8$
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$\begin{array}{l}\phantom{\phantom{;}x^{3}-6x^{2}+12x\phantom{;}-8;}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{3}-6x^{2}+12x\phantom{;}-8\overline{\smash{)}\phantom{;}x^{4}-6x^{3}+12x^{2}\phantom{-;x^n}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}-6x^{2}+12x\phantom{;}-8;}\underline{-x^{4}+6x^{3}-12x^{2}+8x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{4}+6x^{3}-12x^{2}+8x\phantom{;};}\phantom{;}8x\phantom{;}+6\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Integrate the function (x^4-6x^312x^2+6)/(x^3-6x^212x+-8) from 6 to 7. Divide x^4-6x^3+12x^2+6 by x^3-6x^2+12x-8. Resulting polynomial. Expand the integral \int_{6}^{7}\left(x+\frac{8x+6}{x^3-6x^2+12x-8}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{6}^{7} xdx results in: \frac{13}{2}.