Try completing the square on the denominators. you should end up with some arctan in your solution.
I need to integrate this:
1/(x^4+4)
I have that it factors to (x^2+2x+2)(x^2-2x+2). I did the partial fraction decomposition correctly (I think), and I got this:
A=1/8
B=1/4
C=-1/8
D=1/8
I pulled 1/8 from the top of the integrations so I have to integrate:
(1/8)* the integral (x+2)/(x^2+2x+2) - (1/8)*the integral (x+2)/(x^2-2x+2).
That's where I'm stuck. Any help?
Does this seem right?
(1/16)ln(x^2+2x+2) + (1/8)arctan(x+1) + (1/8)arctan(x-1) - (1/16)ln(x^2-2x+2) + C
Something else said it should be -(1/8)arctan(1-x) as the third part instead of +(1/8)arctan(x-1). Which is it?.