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.