Determining whether an improper integral converges or diverges

[aimir]

Hello,
can you plaese halp me with this problem?
I need to determine whether the definite integral of dx/(1+x²sin²(x)), x from 0 to infinity, converges or diverges.
Thank you very much!

 

[renegade05]

diverges

 

[aimir]

Thank you, but can you show me why is it so?
I have to prove it.