Final Answer
Step-by-step Solution
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Divide $2x^3-4x^2-15x+15$ by $x^2-2x+8$
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$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+8;}{\phantom{;}2x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}-2x\phantom{;}+8\overline{\smash{)}\phantom{;}2x^{3}-4x^{2}-15x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+8;}\underline{-2x^{3}+4x^{2}-16x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+4x^{2}-16x\phantom{;};}-31x\phantom{;}+15\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((2x^3-4x^2-15x+15)/(x^2-2x+8))dx. Divide 2x^3-4x^2-15x+15 by x^2-2x+8. Resulting polynomial. Expand the integral \int\left(2x+\frac{-31x+15}{x^2-2x+8}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2xdx results in: x^2.