Integralshard
0:00.0

Determine the value of ∫0111+x3dx\int_{0}^{1} \frac{1}{1+x^3} dx is not elementary, but consider the integral ∫0∞dx1+xn\int_{0}^{\infty} \frac{dx}{1+x^n} for n=3n=3. Which identity relates this to the Beta function B(x,y)=∫01tx−1(1−t)y−1dtB(x, y) = \int_{0}^{1} t^{x-1}(1-t)^{y-1} dt?