How Can We Simplify This Gravitomagnetic Integral?

[olgerm]

$m*\frac{G*16*π*ρ*ω}{c^2}*\int_{a_0}^{a_{1}}(da*a*\int_{y}^{H+y} (\int_0^R (\int_0^{2*π} (\frac{(r-a*Cos(α))*r^2}{(a^2+r^2+h^2-2*r(a*Cos(α)))^{3/2}}* dα)dr)dh))$
This equation is related with this post https://www.physicsforums.com/threads/gravitomagnetic-experiment.824048/.

It where helpful if you could simplify even most inner Integral.

 

[dirk_mec1]

What did you try?

 

[jedishrfu]

The innermost integral is basically A*cos(alpha) / (B + C * cos(alpha)) ^3/2 to be integrated over alpha from 0 to 2pi.

Integral tables may help or you can use u substitution with integration by parts to see if that leads anywhere.