Final answer to the problem
Step-by-step Solution
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Divide $x^2-6x+1$ by $x^2+4x+5$
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$\begin{array}{l}\phantom{\phantom{;}x^{2}+4x\phantom{;}+5;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+4x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{2}-6x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+4x\phantom{;}+5;}\underline{-x^{2}-4x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{-x^{2}-4x\phantom{;}-5\phantom{;}\phantom{;};}-10x\phantom{;}-4\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Integrate the function (x^2-6x+1)/(x^2+4x+5) from 0 to 1. Divide x^2-6x+1 by x^2+4x+5. Resulting polynomial. Expand the integral \int_{0}^{1}\left(1+\frac{-10x-4}{x^2+4x+5}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1}1dx results in: 1.