I have a definite integral (-infinity to +infinity along the real axis) of a rational function with real constant coefficients. Both numerator and denominator are already reduced to linear or irreducible quadratic factors. As I understand it, the integration can always be done by partial fraction decomposition and results in a rational function of the constant coefficients plus possible log and arctan terms.
However, despite every trick I have tried, including assumptions that every constant is real and positive, Mathematica will not complete the job. I am using Mathematica 7 Home Edition.
Here is the function I am trying to integrate over z1:
(4 (A + B z1^2) (A +
B (z1 \[Theta]3 + z Sqrt[1 + \[Theta]3^2])^2))/(\[Pi]^2 (C +
D z1^2)^3 (C + D (z1 \[Theta]3 + z Sqrt[1 + \[Theta]3^2])^2)^3)
Can anyone help?