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