Evaluate ∫−∞∞1x4+x2+1 dx\int_{-\infty}^{\infty} \frac{1}{x^4+x^2+1} \, dx∫−∞∞x4+x2+11dx using residue calculus or algebraic factorization.
π3\frac{\pi}{\sqrt{3}}3π
π2\frac{\pi}{2}2π
2π3\frac{2\pi}{3}32π
π2\frac{\pi}{\sqrt{2}}2π