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## Homework Statement

I'm going through Jackson a bit, reading on Magnetostatics, and I came into a bump.

I'm looking at

[tex]\nabla\times B=\frac{1}{c}\nabla\times\nabla\times\int\frac{j(r')}{|r-r'|}d^3r'[/tex]

I expand that using 'BAC-CAB' rule and I get:

[tex]\nabla\times B=\frac{1}{c}\nabla\int j(r')\cdot\nabla\left(\frac{1}{|r-r'|}\right)d^3r'-\frac{1}{c}\int j(r')\nabla^2\left(\frac{1}{|r-r'|}\right)d^3r'[/tex]

So after changing the [tex]\nabla[/tex] into [tex]\nabla '[/tex] and using the fact that [tex]\nabla^2\left(\frac{1}{|r-r'|}\right)=-4\pi\delta(r-r')[/tex]

I end up with:

[tex]\nabla\times B=-\frac{1}{c}\nabla\int j(r')\cdot\nabla '\left(\frac{1}{|r-r'|}\right)d^3r'+\frac{4\pi}{c}j(r)[/tex]

And here it says that the first part after integration by parts becomes:

[tex]\nabla\times B=\frac{1}{c}\nabla\int \frac{\nabla '\cdot j(r')}{|r-r'|}\right)d^3r'+\frac{4\pi}{c}j(r)[/tex]

I tried integration by parts like this:

[tex]j(r')d^3r'=dv\Rightarrow j(r')=v[/tex] and [tex]\nabla '\left(\frac{1}{|r-r'|}\right)=u\Rightarrow \nabla^2'\left(\frac{1}{|r-r'|}\right)d^3r'=du[/tex]

But I don't get what I need :\

What am I doing wrong?