Final Answer
Step-by-step Solution
Specify the solving method
We could not solve this problem by using the method: Integrate by substitution
Divide $2x^3-4x^2-15x+5$ by $x^2-2x-8$
Learn how to solve definite integrals problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}-8;}{\phantom{;}2x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}-2x\phantom{;}-8\overline{\smash{)}\phantom{;}2x^{3}-4x^{2}-15x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-8;}\underline{-2x^{3}+4x^{2}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{-2x^{3}+4x^{2}+16x\phantom{;};}\phantom{;}x\phantom{;}+5\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve definite integrals problems step by step online. Integrate the function (2x^3-4x^2-15x+5)/(x^2-2x+-8) from 1 to 3. Divide 2x^3-4x^2-15x+5 by x^2-2x-8. Resulting polynomial. Expand the integral \int_{1}^{3}\left(2x+\frac{x+5}{x^2-2x-8}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{1}^{3}2xdx results in: 8.