IMPROPER INTEGRALS: INFINITE INTERVAL $OF$ INTEGRATION

Resin$\{Im(z)>0\},{\displaystyle \underset{-}{\overset{}{}}}\frac{dx}{(1+x^2{)}^3}$

Even function trick ${\displaystyle \underset{0}{\overset{}{}}}\frac{dx}{1+x^4}$

Fourier Integral ${\displaystyle \underset{-}{\overset{}{}}}\frac{cos2x}{(x^2+1{)}^2}dx$

Fourier Integral ${\displaystyle \underset{-}{\overset{}{}}}\frac{sin3x}{x^4+1}dx$