Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $x^3-2x+3$ by $x^2-2x-3$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}-3;}{\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-3;}\underline{-x^{3}+2x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+2x^{2}+3x\phantom{;};}\phantom{;}2x^{2}+x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-3-;x^n;}\underline{-2x^{2}+4x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;-2x^{2}+4x\phantom{;}+6\phantom{;}\phantom{;}-;x^n;}\phantom{;}5x\phantom{;}+9\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3-2x+3)/(x^2-2x+-3))dx. Divide x^3-2x+3 by x^2-2x-3. Resulting polynomial. Expand the integral \int\left(x+2+\frac{5x+9}{x^2-2x-3}\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.