Determine the value of ∫0∞1x3+1dx\int_{0}^{\infty} \frac{1}{x^3+1} dx∫0∞x3+11dx.
2π33\frac{2\pi}{3\sqrt{3}}332π
π33\frac{\pi}{3\sqrt{3}}33π
4π33\frac{4\pi}{3\sqrt{3}}334π
π3\frac{\pi}{\sqrt{3}}3π