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