I would like to evaluate the following integral $$\int_{-2}^{-1} \frac{x+1}{x^2(x-1)} dx$$
I tried to solve it by partial fractions as $$\int_{-2}^{-1} \left(\frac2x + \frac{-1}{x^2} + \frac{-2}{x-1} \right)dx $$ and I got $$2\left.\ln{\frac1{x-1}}\right|_{-2}^{-1} $$ it to be $2\ln({3\over 2})$. But the right solution is $2\ln \left({4\over 3} \right)-{1\over 2}$. Where did I go wrong?