Consider the below integral $$ \iint \phi_a(r_1)\,\phi_b(r_2)\, \nabla_1\, \nabla_2\, \phi_c(r_1)\, \phi_d(r_2)\, dr_1\, dr_2 $$ where the bounds of the integrals are $-\infty$ to $+\infty$. Is it always true that rewrite this as follows?
$$ =\int\phi_a(r_1)\,\nabla_1\, \phi_c(r_1)\,dr_1\, \int\phi_b(r_2)\,\nabla_2\, \phi_d(r_2)\,dr_2 $$