I must solve $$\int_{-\infty}^{\infty}\frac{x \text{sin}x}{x^2+4} dx$$ I simplified this to $$\int_{-\infty}^{\infty}\frac{x \text{sin}x}{x^2+4} dx = \frac{1}{i}\int_{-\infty}^{\infty}\frac{x e^{ix}}{x^2+4} dx$$ Now consider only $$\int_{-\infty}^{\infty}\frac{x e^{ix}}{x^2+4} dx $$ I considered ...