Let's see some cool application of contour integral first.
1. ∫R1/(1+x2)dx\int_\R 1/(1+x^2) dx∫R1/(1+x2)dx
didn't finish, the rest will wait till next week.
2. ∫0∞1/(1+x3)dx\int_0^\infty 1/(1+x^3) dx∫0∞1/(1+x3)dx
3. ∫0∞e−x/(1+x3)dx\int_0^\infty e^{-x}/(1+x^3) dx∫0∞e−x/(1+x3)dx
4. ∫Rxx4+1e−x2dx\int_\R \frac{x}{x^4+1} e^{-x^2} dx∫Rx4+1xe−x2dx