\int \frac{2x^{2}+5x-1}{x^{3}+x^{2}-2x}dx=\frac{1}{2}\int \frac{dx}{x}+2\int \frac{dx}{x-1}-\frac{1}{2}\int\frac{dx}{x+2}=\frac{1}{2}\ln (x)+2\ln (x-1)-\frac{1}{2}\ln (x+2)+C\