I have a mathematical question that arose from a physics problem.
In the derivation of torque $N$ for a stable charge distribution $\varrho(\vec{r})$ that is the cause of a constant electric field $\vec{E}_{0}$ the following transformation is given:
$$\vec{N}=\int \vec{r} \times\left(\varrho(\vec{r}) \vec{E}_{0} d^{3} \vec{r}\right)=\vec{p} \times \vec{E}_{0}$$
$\vec{p}=\int \varrho\left(\overrightarrow{r^{\prime}}\right) \overrightarrow{r^{\prime}} d^{3} \overrightarrow{r^{\prime}}$ is the dipole-moment.
How would you justify the following transformation?
$$\int \vec{r} \times\left(\varrho(\vec{r}) \vec{E}_{0} d^{3} \vec{r}\right)=\left(\int \vec{r}\varrho(\vec{r})d^{3}\vec{r} \right) \times\left( \vec{E}_{0} \right)$$