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