Problem 1705 (difficulty: 7/10)

\(\displaystyle \int_0^\infty\frac\dx{x^3+1}=? \quad \int_0^\infty\frac{\log x}{x^2+x+1}\dx=? \quad \int_0^\infty\frac{\log^2x}{x^2+1}\dx=? \)

Give me another random problem!