Final answer to the problem
Step-by-step Solution
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Divide $x^4-3x^3-5x^2+8x-1$ by $x^3-2x^2-8x$
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$\begin{array}{l}\phantom{\phantom{;}x^{3}-2x^{2}-8x\phantom{;};}{\phantom{;}x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}x^{3}-2x^{2}-8x\phantom{;}\overline{\smash{)}\phantom{;}x^{4}-3x^{3}-5x^{2}+8x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}-2x^{2}-8x\phantom{;};}\underline{-x^{4}+2x^{3}+8x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3}+8x^{2};}-x^{3}+3x^{2}+8x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{3}-2x^{2}-8x\phantom{;}-;x^n;}\underline{\phantom{;}x^{3}-2x^{2}-8x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}-2x^{2}-8x\phantom{;}-;x^n;}\phantom{;}x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((x^4-3x^3-5x^28x+-1)/(x^3-2x^2-8x))dx. Divide x^4-3x^3-5x^2+8x-1 by x^3-2x^2-8x. Resulting polynomial. Expand the integral \int\left(x-1+\frac{x^{2}-1}{x^3-2x^2-8x}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2.