Final Answer
Step-by-step Solution
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Divide $2x^3-6x+3$ by $x^2+1$
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$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}2x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}2x^{3}\phantom{-;x^n}-6x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-2x^{3}\phantom{-;x^n}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}-2x\phantom{;};}-8x\phantom{;}+3\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Integrate the function (2x^3-6x+3)/(x^2+1) from 0 to 2. Divide 2x^3-6x+3 by x^2+1. Resulting polynomial. Expand the integral \int_{0}^{2}\left(2x+\frac{-8x+3}{x^2+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2}2xdx results in: 4.