Final Answer
Step-by-step Solution
Specify the solving method
Divide $x^5+3x^4-x^3-4x^2-6x-1$ by $x^3+3x^2-x-3$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{3}+3x^{2}-x\phantom{;}-3;}{\phantom{;}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;}x^{3}+3x^{2}-x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{5}+3x^{4}-x^{3}-4x^{2}-6x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{3}+3x^{2}-x\phantom{;}-3;}\underline{-x^{5}-3x^{4}+x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-3x^{4}+x^{3}+3x^{2};}-x^{2}-6x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^5+3x^4-x^3-4x^2-6x+-1)/(x^3+3x^2-x+-3))dx. Divide x^5+3x^4-x^3-4x^2-6x-1 by x^3+3x^2-x-3. Resulting polynomial. Expand the integral \int\left(x^{2}+\frac{-x^{2}-6x-1}{x^3+3x^2-x-3}\right)dx into 2 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}.