I have to evaluate an integral of this form $$\int\int\int \nabla^2f(r, \theta, \phi)r^2\sin\theta drd\theta d\phi$$ where $\nabla^2$ which has partial derivatives, is in spherical coordinates.
Would the $\nabla^2$ operate on the $f(r, \theta, \phi)$ only or also on the $r^2\sin\theta$?
Context:I got this from solving a Physics problem involving $\langle\psi|\hat O|\psi\rangle $ where $\hat O$ contains $\nabla^2$, so $$\langle\psi|\hat O|\psi\rangle = \int\psi^*\nabla^2\psi dV$$