I would like to evaluate an integrale which depend on 2 parameters. The goal is to obtain an expression of the integrale depending on theses 2 parameters ($x_d$ and $z_d$) such as $f(x_d,z_d)= \ldots$.
$$ \int_{-\infty}^{\infty}{\frac{1}{\sqrt{(x^2+1)^3\cdot [(x - x_d)^2+(1-z_d)^2]^3}}}dx$$
The range of $z_d$ is [-6,0.8] and the range of $x_d$ is [-10,10]. The idea is to have the value of this integral for any combination of $(x_d,z_d).$
I tried integration by parts, partial fraction decomposition, integration by susbstitution..
Do you have any idea ? Do you think that such an expression $f(x_d,z_d)$ can be obtained ?