$$R(t)=\int_{-\infty}^\infty\dfrac{\omega e^{i\omega t}}{(3-\omega^2)^{2}+4\omega^2}\,d\omega$$
where t is a integer and $t>0$
I used to calculate this integral by numerical integral,but it seems that using ifft in matlab is more effcient.
The ifft equation in Matlab is $$x(n)=\frac{1}{N}\sum_{k=1}^N X(k)e^{i2\pi\frac{k-1}{N}n-1}$$ where n=$1,2...,N$
I have no idea how to link the above Eq with the above-mentioned integral. Do someone have an idea?