# Thread: integral of ratio of cosine and polynomial

1. ## integral of ratio of cosine and polynomial

hi there,

i have problems solving the following integral:

\int_{-\infty}^{\infty} \dfrac{\cos(x\k)}{x^2+k^4}\,dx

i could not come up with an appropriate substitution (even for k = 1). i also tried integration via Euler's formula - could not work that out either.

anybody an idea on how to attack this problem? many thanks in advance!!!

best,
Stefan

2. (Hi, you can put t=kx then use residues).
Sorry, t=x/k is better.

3. Originally Posted by girdav
Hi, you can put t=kx then use residues.
ok, i see. thanks a lot for your support, it's really much appreciated!

best,
Stefan