Determine the value of ∫0111+x3 dx\int_0^1 \frac{1}{\sqrt{1+x^3}} \, dx∫011+x31dx in terms of Beta functions.
13B(13,12)\frac{1}{3} B(\frac{1}{3}, \frac{1}{2})31B(31,21)
12B(13,12)\frac{1}{2} B(\frac{1}{3}, \frac{1}{2})21B(31,21)
13B(12,12)\frac{1}{3} B(\frac{1}{2}, \frac{1}{2})31B(21,21)
16B(13,12)\frac{1}{6} B(\frac{1}{3}, \frac{1}{2})61B(31,21)