Hi,

while trying to evaluate below

$\displaystyle

\int_{-\infty}^{\infty} \! \frac{\sin{x}}{x} \, dx

$

I was hoping to use

1. Use complex numbers i.e pole at x=0

$\displaystyle

\int_{-\infty}^{\infty} \! f(x) \, dx = 2\pi\, i \sum_{res\, upper\, hp} {f(x)} \, + \pi\, i \sum_{res\, real\, axis} {f(x)}

$

which gives 0

2. Expand by sin(x) by Taylor series around 0 and multiply by x

this gives a divergent series

which one is correct?

thanks