$$I(x)=\int\frac{-x+5}{(x^{2}-x-2)(x-2)}dx$$
$\left\{\begin{matrix}I=\frac{2x\ln(|x+1|)-2x\ln(|x-2|)-4\ln(|x+1|)+4\ln(|x-2|)-3}{3x\left(x-2\right)}+\frac{С\left(x-2\right)}{x^{2}-2x}\text{, }&x\neq -1\text{ and }x\neq 2\text{ and }x\neq 0\\I\in \mathrm{R}\text{, }&С=\frac{2\ln(2)}{3}-\frac{1}{2}\text{ and }x=0\end{matrix}\right.$
