Evaluate ∫0∞x21+x4dx\int_0^{\infty} \frac{x^2}{1+x^4} dx∫0∞1+x4x2dx using the residue theorem or symmetry.
π22\frac{\pi}{2\sqrt{2}}22π
π2\frac{\pi}{\sqrt{2}}2π
π4\frac{\pi}{4}4π
π2\frac{\pi}{2}2π