Find the Volume of the Resulting Solid If the Region $$y = \frac { 1 } { \left( x ^ { 2 } + 3 x + 2 \right) }$$

Short Answer

Find the volume of the resulting solid if the region under the curve
$$y = \frac { 1 } { \left( x ^ { 2 } + 3 x + 2 \right) }$$
from $x = 0$ to $x = 1$ is rotated about the $x$ -axis. Round your answer to four decimal places.