line integral to solid angle

>We start with the line integral.

Then we can make a transformation by using the following identity.

Not for the second step, the second term on the right went away because the line integral is not a function of the unprimed coordinates. That is the same reason we can pull the curl out of integral.

Now we have a form that we can use an integral theorem.

From here we can use a triple product rule for the curl and then we have to take care of psi specifically.