Determine the value of ∫0∞1x2+2x+2dx\int_0^{\infty} \frac{1}{x^2+2x+2} dx∫0∞x2+2x+21dx.
π2\frac{\pi}{2}2π
π4\frac{\pi}{4}4π
π8\frac{\pi}{8}8π
π6\frac{\pi}{6}6π