Question

How do you use partial fractions to find the integral `int (2x^2-2x+3)/(x^3-x^2-x-2)dx`?

Answer 1

By substituting small numbers as a guess, `x=2` makes the denominator zero, so the partial fraction expression, by the cover up rule, is
`(7/7)/(x-2)+(Ax+B)/(x^2+x+1)`

Explanation:

Then equating powers of `x` you get `A=1`, `B=-1`. The second term is now linear divided by quadratic which is routine.