We consider the biquaternionic equation $\operatorname{curl}\vec{w}+\lambda\vec {w}=\vec g,\,\lambda\in\mathbb{C},\,\lambda\neq0$ over bounded and unbounded domains $\Omega$ in $\mathbb{R}^{3}$ and $\vec g$ an integrable function whose divergence is also integrable. A general solution of the equation is given in terms of classical integral operators as well as some applications.