Answer
$-\ln |x-1|+2 \ln |x-2| +c$
Work Step by Step
Integration by parts formula suggests that $\int p'(x) q(x)=p(x) q(x)-\int p(x) q'(x)dx$
$\int \dfrac{x}{x^2-3x+2}=\int \dfrac{x}{(x-1)(x-2)}$
Write the integral into partial fractions as follows: $\int \dfrac{x}{(x-1)(x-2)}=\int [\dfrac{-1}{(x-1)}+\dfrac{2}{(x-2)}]dx$
Hence, $\int \dfrac{x}{(x-1)(x-2)}=-\ln |x-1|+2 \ln |x-2| +c$
