How to solve the following integrand: $$\int^\infty_{-\infty}\frac{\sin x}{x} dx\;?$$ I know how to evaluate it by using the path of a rectangle, but it is too difficult and would make some mistakes.
I am wondering if there is a simpler way to solve questions like this. Thanks！
This integral is known as the Dirichlet Integral (or at least it almost is), and there are several ways to solve it that vary in dificulty depending on what techniques you know, though contour integration is one of the simpler ones.