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