Determine the value of ∫0∞dx(1+x2)2\int_0^{\infty} \frac{dx}{(1+x^2)^2}∫0∞(1+x2)2dx.
π4\frac{\pi}{4}4π
π2\frac{\pi}{2}2π
111
π8\frac{\pi}{8}8π