I'm trying to solve the following integral : $$\iiint_E \exp\left(-a \lVert\vec{OC}\rVert\right)\,\mathrm{d}V = \iiint_E \exp\left(-a \sqrt{(x-x_c)^2+(y-y_c)^2+(z-z_c)^2}\right)\,\mathrm{d}V$$
With $E$ being a cylinder (if a solution for a sphere exists as well, I'm interested) and $C (x_c, y_c, z_c)$ a point outside of the cylinder.
I found a few answers on mathexchange regarding this sort of integral for a sphere when $C$ is the center of the sphere (ex), but I could not find anything for a C outside of the sphere.
Wolfram|alpha did not find any solutions.
The objective is to be able to calculate auto attenuation effect in a cylinder source for direct line attenuation.
Any help would be appreciated. Thanks!
I might be totally incorrect, as I haven't seen calculus in a long time, but I would think it would be a good opportunity to change to cylindrical coordinates and use the jacobian.
If this isn't toally nonsense, I'd be happy to try and write it for you assuming dV=dxdydz and xc, yc, zc, and a are constants.