Partial Fraction Integrals

Hey i've got 3 integrals i need to solve which are the following.

$\displaystyle \int \frac{x^2-2}{(x+1)(x-2)}$

$\displaystyle \int \frac{x-1}{(x+1)(x-2)^2}$

$\displaystyle \int \frac{1}{(x+1)(x^2+2x+2)}$

For every other example i've done, before I convert the fraction to something I can integrate the question tells me what form to put the equation in.

So my question is how do i know what form do i have to put the fraction in before i integrate i.e.

$\displaystyle \int \frac{x^2-2}{(x+1)(x-2)} = \int \frac{A}{x+1} +\int \frac{Bx+C}{x-2}$

or would it be something like

$\displaystyle \int \frac{x^2-2}{(x+1)(x-2)} = \int A + \int \frac{Bx+C}{x+1} + \int\frac{D}{x-2}$