Integrate 1/(t^2+1)^2 Using i and Partial Fractions

[cragar]

i was trying to integrate \frac{1}{(t^2+1)^2}
By factoring it into \frac{1}{(t+i)^2(t-i)^2} and then doing partial fractions.
then integrating each term using a u substitution. Ok but then how do I get the real part out of this solution. I know the arctan(t) can be extracted out of stuff of this form.

 

[lurflurf]

use
$$\arctan(x)=\tfrac{1}{2}\imath \, (\log(1-\imath\, x)-\log(1+\imath\, x))$$