I am trying to evaluate $\displaystyle\int\limits_0^{\infty}\displaystyle\frac{e^{iwx}}{(x+a)^2+b^2}\,dx$ where $w$, $a$ and $b$ are positive real numbers. I tried to use the contour integration but since the integral limits are from $0$ to $\infty$ I am not sure which contour I need to use. Does anybody have any idea how to evaluate this integral? Thanks.
2026-03-29 20:27:41.1774816061
Evaluating integral $\int\limits_0^{\infty}\frac{e^{iwx}}{(x+a)^2+b^2}\,dx$ with contour integral
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