\int{{\varphi^2+\rho^2x^2}\over\sqrt{\varphi^2+\rho^2x^2}}{dx}=\int{{\varphi^2}\over\sqrt{\varphi^2+\rho^2x^2}}{dx}+\int{{\rho^2x^2}\over\sqrt{\varphi^2+\rho^2x^2}}{dx}