Hmm, that seems to make sense, but it gets me to an integral I'm not having much more luck with. The only thing I can think of is some other subsitution that I can't figure out.
[tex]  2k\int {\frac{{t^8  4t^6 + 2(8k  5)t^4  4t^2 + 1}}{{(1 + t^2 )^3 (1  \frac{{4kt^2 }}{{(1 + t^2 )^2 }})^\frac {3}{2} }}} [/tex]
Making [tex] u=1  \frac{{4kt^2 }}{{(1 + t^2 )^2 }} [/tex] almost seems to work, but not quite. Any advice on what to do from here?
