Find the integral $\int\frac{-8x^3+10x^2-15x+10}{2x^2+x+8}dx$

Learn how to solve integrals of rational functions problems step by step online.

$\begin{array}{l}\phantom{\phantom{;}2x^{2}+x\phantom{;}+8;}{-4x\phantom{;}+7\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}+x\phantom{;}+8\overline{\smash{)}-8x^{3}+10x^{2}-15x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}+x\phantom{;}+8;}\underline{\phantom{;}8x^{3}+4x^{2}+32x\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}8x^{3}+4x^{2}+32x\phantom{;};}\phantom{;}14x^{2}+17x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}+x\phantom{;}+8-;x^n;}\underline{-14x^{2}-7x\phantom{;}-56\phantom{;}\phantom{;}}\\\phantom{;-14x^{2}-7x\phantom{;}-56\phantom{;}\phantom{;}-;x^n;}\phantom{;}10x\phantom{;}-46\phantom{;}\phantom{;}\\\end{array}$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((-8x^3+10x^2-15x+10)/(2x^2+x+8))dx. Divide -8x^3+10x^2-15x+10 by 2x^2+x+8. Resulting polynomial. Expand the integral \int\left(-4x+7+\frac{10x-46}{2x^2+x+8}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int-4xdx results in: -2x^2.