I am trying to integrate: (xa-ia+yb-jb+zc-kc)/((x-I)^2+(y-j)^2+(z-k)^2)^(3/2)dxdydz from generic x y and z initiqls to finals. I have completed part of it, but I am stick on the part dx/(x^2-2xi+i^2+f)^(3/2) The initial formula is not complete, right now I am primarily honeing my integration, so please show me your work as best you can.
A b and c are componentes of a surface normal and i j and k are the position of the pixel. X y and z are points inside the rectangular prism light.
I found the answer to dx/(x^2-2xi+i^2+f)^(3/2), which is (cx-ic)/(f(x^2-2ix+I^2+f)^(1/2)), but now I am stuck on ( (y-j)d+af)/(((y-j)^2+a^2)(b^2+(y-j)^2+a^2)^(1/2))dy This integral seems worse than the last.