Final Answer
Step-by-step Solution
Specify the solving method
Divide $5x^3-15x-4x^2+5$ by $x^2-2x-8$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}-8;}{\phantom{;}5x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}-8\overline{\smash{)}\phantom{;}5x^{3}-4x^{2}-15x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-8;}\underline{-5x^{3}+10x^{2}+40x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{3}+10x^{2}+40x\phantom{;};}\phantom{;}6x^{2}+25x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-8-;x^n;}\underline{-6x^{2}+12x\phantom{;}+48\phantom{;}\phantom{;}}\\\phantom{;-6x^{2}+12x\phantom{;}+48\phantom{;}\phantom{;}-;x^n;}\phantom{;}37x\phantom{;}+53\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((5x^3-15x-4x^2+5)/(x^2-2x+-8))dx. Divide 5x^3-15x-4x^2+5 by x^2-2x-8. Resulting polynomial. Expand the integral \int\left(5x+6+\frac{37x+53}{x^2-2x-8}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5xdx results in: \frac{5}{2}x^2.