# Thread: Determining whether an improper integral converges or diverges

1. ## Determining whether an improper integral converges or diverges

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!

2. ## Re: Determining whether an improper integral converges or diverges

I didn't think a lot about the problem, but it seems you have to study the convergence of the series $\sum_{n=0}^{+\infty}a_n$ where $a_n=\int_0^{\pi}\frac{dt}{1+(n\pi+t)^2\sin^2tdt}$.