Hello,

You can see here : http://www.mathhelpforum.com/math-he...-integral.html for something similar, proving it's convergent.

(similar method as (1-cos)/x²)

As for the integration by parts, integrate 1/x² and differentiate sin²(x) (which will give 2sin(x)cos(x), and this is where you'll use the identity)

And this would rather be int(sin(2x)/x), wouldn't it ?