hi again!

i have to make partialfractions out of the following integral:

$\displaystyle \int \frac{1-x}{x^3-2x^2+x-2} dx$

guessing a critical point for the denominator gives me $\displaystyle x_{0}=2$

then polynomial division gives me

$\displaystyle (x^3-2x^2+x-2) / (x-2) = x^2+1$

$\displaystyle \rightarrow \frac {1-x}{(x-2)(x^2+1)} = \frac {A}{x-2} + \frac{B}{x^2+1}$

is this correct ? if so, i dont seem to get an equation system that is solvable...

could you give me a quick hint to do partial fractions in general ? like the different cases etc..., my professors script is a mess

thanks