Final Answer
Step-by-step Solution
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Divide $x^3+x^2-12x+1$ by $x^2+x-12$
Learn how to solve definite integrals problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}-12;}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}+x\phantom{;}-12\overline{\smash{)}\phantom{;}x^{3}+x^{2}-12x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-12;}\underline{-x^{3}-x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2}+12x\phantom{;};}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve definite integrals problems step by step online. Integrate the function (x^3+x^2-12x+1)/(x^2+x+-12) from 0 to 2. Divide x^3+x^2-12x+1 by x^2+x-12. Resulting polynomial. Expand the integral \int_{0}^{2}\left(x+\frac{1}{x^2+x-12}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2} xdx results in: 2.