Determine the value of ∫01dx1+x3\int_0^1 \frac{dx}{1+x^3}∫011+x3dx.
13ln2+π33\frac{1}{3} \ln 2 + \frac{\pi}{3\sqrt{3}}31ln2+33π
13ln2\frac{1}{3} \ln 231ln2
π33\frac{\pi}{3\sqrt{3}}33π
12ln2+π6\frac{1}{2} \ln 2 + \frac{\pi}{6}21ln2+6π