General form of a central force is F(r)=F(r) (r^)

[Note that This form of central force satisfies L=rxp=0 as well]

But the isotropic or centro-symmetric form is

F(r)=F(r) (r^)

I found in a book that the second form of a central force is conservative.OK,this can be proved easily.What about the first expression?It is NOT centro-symmetric...depends on the position vector r it is acting on.

Why is it NOT conservative always?

Actually,I am not sure whether the same curl operation will do...Please check it...I am getting stuck in the differentiation of the r vector wihin the bracket while taking the curl.I feel confusion if the curl in two cases can be done in exactly similar way.