You have basically a triple integral which can be solved by integral3. This means you have to first calculate J(r)*curl(r) analytically, so taking vector product from nabla times r to get the curl. Then you take the dot product with J(r) where you will end up with a scalar function. Finally you define this function in an own .m-file or as anonymous function before putting everything into integral3.
Give some more information on the exact function, if you need more help