Show $\int _ { 0 } ^ { \infty } \frac { x \sin x } { \left( x ^ { 2 } + 1 \right) ^ { 2 } } dx = \frac { \pi } { 4 e }$ with residue theorem
Calculating the integral $\int_{-\infty}^{\infty} x\sin(x)/(x^2+1)^2 dx$