Question

Solve :$\int \frac{2x^3-3x^2-8x-26}{2x^2-5x+2}dx$

Answer 1

$\int \frac{2x^3-3x^2-8x-26}{2x^2-5x+2}dx=\int x+1+\frac{-5x-28}{2x^2-5x+2}dx=\int xdx+1\int dx+\int \frac{-5x-28}{2x^2-5x+2}dx=\frac{x^2}{2}+x-10(\frac{1}{8}log[16x^2-40x+16]-\frac{5}{24}\left(log[\frac{-2}{3}+\frac{4x}{3}]\right)-log[\frac{-8}{3}+\frac{4x}{3}])-28(\frac{1}{3}log[x-2]-\frac{1}{3}log[2x-1])+C$