calculate complex integral of a sum



Hi,

integrate(sum(1/(n^4+x^2), n, 1, inf),x,0,inf);

by hand + using maxima to calculate some small parts of it,
I eventually reached the result, which is pi^3/12.

I wonder if it is possible to calculate in maxima straight off. Is it?

What I did, was replacing by hand arctan(0) with 0, separately
calculating limits and so on. Took a bit of time, and mostly I did it
myself on paper, just checking some parts with maxima. But still I'm
not even sure if my final result is correct ;)

question is - how to do it in a "clean" way in maxima?

-- 
Janek Kozicki                               http://janek.kozicki.pl/  |