1. ## simple integration

$

\int^{\infty}_{-\infty}x^{-1/2}e^{x/2}dx
$

2. Edit: sorry it was wrong

3. Hello,

This is weird because it is not defined for x<0...

$

\int^{\infty}_{-\infty}x^{-1/2}e^{x/2}dx
$
Well intuitively when say x>1, $e^{x/2}$ grow faster then $\sqrt{x}$ . It follows that $\int_1^\infty \frac{e^{x/2}}{\sqrt{x}}\,dx$ diverges and hence so is the original integral.