Volume of revolution involving arctan

Find the volume of the solid of revolution formed when the area between the curve $y = \sqrt{\dfrac{\arctan(x)}{1+x^2}}$ and the $x$-axis from $x = 1$ to $x = \sqrt{3}$ is rotated about the $x$-axis.

Give your answer in the form $\dfrac{a\pi^b}{c}$, where $a, b, c \in Z^+$.