r(hat)/r^2 cross r'(hat)/r'^2 integration (solved, nevermind)
\(\displaystyle \displaystyle \int_{-\infty}^{\infty}\,\int_{-\infty}^{\infty}\,\int_{-\infty}^{\infty}\, \left(x^2\, +\, y^2\, +\, z^2\right)^{-3/2}\, \times\, \dfrac{1}{\sqrt{\strut (x\, +\, d)^2\, +\, y^2\, +\, z^2\,}}\,(x,\, y,\, z)\, \times\, (x\, +\, d,\, y,\, z)\, dx\, dy\, dx\)
or
(x^2 + y^2 + z^2)^(-1/2) ((x + d)^2 + y^2 + z^2)^(-3/2) (x, y, z)x(x + d, y, z) integrate over all xyz
since I don't know how to code, a link to wolfram alpha with the equation (that it doesn't want to compute):
https://www.wolframalpha.com/input/?i=int+(x%5E2%2By%5E2%2Bz%5E2)%5E(-3%2F2)*((x%2Bd)%5E2%2By%5E2%2Bz%5E2)%5E(-1%2F2)+(x,y,z)+cross+(x%2Bd,y,z)+dx+dy+dz,+x%3D-infinity+to+infinity,+y%3D-infinity+to+infinity,+z%3D-infinity+to+infinity
I'm pretty stuck on this. Halp:?:
Edit: found the solution. Put it in spherical coordinates, change the d(theta) to du=sin(theta) dcos(theta), integrate r first, then integrate u.
\(\displaystyle \displaystyle \int_{-\infty}^{\infty}\,\int_{-\infty}^{\infty}\,\int_{-\infty}^{\infty}\, \left(x^2\, +\, y^2\, +\, z^2\right)^{-3/2}\, \times\, \dfrac{1}{\sqrt{\strut (x\, +\, d)^2\, +\, y^2\, +\, z^2\,}}\,(x,\, y,\, z)\, \times\, (x\, +\, d,\, y,\, z)\, dx\, dy\, dx\)
or
(x^2 + y^2 + z^2)^(-1/2) ((x + d)^2 + y^2 + z^2)^(-3/2) (x, y, z)x(x + d, y, z) integrate over all xyz
since I don't know how to code, a link to wolfram alpha with the equation (that it doesn't want to compute):
https://www.wolframalpha.com/input/?i=int+(x%5E2%2By%5E2%2Bz%5E2)%5E(-3%2F2)*((x%2Bd)%5E2%2By%5E2%2Bz%5E2)%5E(-1%2F2)+(x,y,z)+cross+(x%2Bd,y,z)+dx+dy+dz,+x%3D-infinity+to+infinity,+y%3D-infinity+to+infinity,+z%3D-infinity+to+infinity
I'm pretty stuck on this. Halp:?:
Edit: found the solution. Put it in spherical coordinates, change the d(theta) to du=sin(theta) dcos(theta), integrate r first, then integrate u.
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