\(\int \frac{2x^{3} -10x^{2} +16x-1}{x^{2} -5x+6} {\rm d}x \)
\(=\int \left(2x+\frac{4x-1}{\left(x-2\right)\left(x-3\right)} \right){\rm d}x \)
\(=\int \left(2x-\frac{7}{x-2} +\frac{11}{x-3} \right){\rm d}x \)
\(=\frac{x^{2} }{2} -7\ln \left|x-2\right|+11\ln \left|x-3\right|+C\)