Final answer to the problem
Step-by-step Solution
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Divide $x^2+1$ by $x^2-x$
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$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;};}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;};}\underline{-x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+x\phantom{;};}\phantom{;}x\phantom{;}+1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve problems step by step online. Find the integral int((x^2+1)/(x^2-x))dx. Divide x^2+1 by x^2-x. Resulting polynomial. Expand the integral \int\left(1+\frac{x+1}{x^2-x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dx results in: x.