Can I express the integral $\int_0^1[\cos (xt)/(1-t^2)]dt$ in terms of Bessel Polynomial? I tried by putting $t=\sin \theta$ and used the integral representation of Bessel's polynomial $J_n(x)=(1/\pi)\int_0^\pi \cos(n\theta-x\sin \theta)d\theta$. I expect the answer may be $J_0(x)(\pi/2)$. But I did not get it even now. Help is solicited.