Your integral is $\displaystyle \int_0^{\sqrt{3}}\sqrt{9t^4+9t^2}\,dt $ right? So $\displaystyle \int_0^{\sqrt{3}}\sqrt{9t^2\left(t^2+1\right)}\,dt $. Now bring the $\displaystyle 9t^2$ out from the square root.
Your integral is $\displaystyle \int_0^{\sqrt{3}}\sqrt{9t^4+9t^2}\,dt $ right? So $\displaystyle \int_0^{\sqrt{3}}\sqrt{9t^2\left(t^2+1\right)}\,dt $. Now bring the $\displaystyle 9t^2$ out from the square root.