Question

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

Answer 1

$\int \frac{2x^3-3x^2-8x-26}{2x^2-5x+2}dx=\int (\frac{-5x-28}{2x^2-5x+2}+x+1)dx=-\int \frac{5x+28}{2x^2-5x+2}dx+\int xdx+\int 1dx=-\int (\frac{5(4x-5)}{4(2x^2-5x+2)}+\frac{137}{4(2x^2-5x+2)})dx+\frac{x^2}{2}+x=\frac{5}{4}\int \frac{4x-5}{2x^2-5x+2}dx+\frac{137}{4}\int \frac{1}{2x^2-5x+2}dx+\frac{x^2}{2}+x=\frac{5\log (2x^2-5x+2)}{4}-\frac{137\log (2x-1)}{12}+\frac{13\log (x-2)}{12}+\frac{x^2}{2}+x+C=\frac{61\log (2x-1)+3x(x+2)-76\log (x-2)}{6}+C$