Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $x^3-4x-10$ by $x^2-x-6$
Learn how to solve definite integrals problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}-6;}{\phantom{;}x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}-6\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}-4x\phantom{;}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}-6;}\underline{-x^{3}+x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+x^{2}+6x\phantom{;};}\phantom{;}x^{2}+2x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}-6-;x^n;}\underline{-x^{2}+x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;-x^{2}+x\phantom{;}+6\phantom{;}\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}-4\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve definite integrals problems step by step online. Integrate the function (x^3-4x+-10)/(x^2-x+-6) from 0 to 1. Divide x^3-4x-10 by x^2-x-6. Resulting polynomial. Expand the integral \int_{0}^{1}\left(x+1+\frac{3x-4}{x^2-x-6}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1} xdx results in: \frac{1}{2}.