I need to use partial fractions on this term:

$\displaystyle

\dfrac {1} {(s + 1)[(s-1)^2 +1]}

$

this term (note: it said $\displaystyle \omega \neq 4)$:

$\displaystyle

\dfrac {s} {(s^2 + 4)(s^2 + \omega ^2)} + \dfrac {s} {(s^2 + \omega ^2)}

$

and lastly this term

$\displaystyle

\dfrac {s-3} {s^2 - 4s + 4} = \dfrac {a} {(s-2)^2} + \dfrac {b} {s-2}

$

I am stumped because I have tried all the methods that worked on the prior problems (which were easier no doubt) but I keep running into an impasse. Can anyone please help? I'm in differential equations (doing the chapter on LaPlacian's) but this is definitely from calculus. Thank you!

Kind Regards,

Andy