Problem 1717 (difficulty: 6/10)

\(\displaystyle \int_0^\infty\frac{\sqrt{x}}{x^3+1}\dx=? \quad \int_{-\infty}^\infty\frac{e^{-it}}{x^4+1}=? \quad \int_0^\infty\frac{\sin x}x\dx=? \)

Give me another random problem!