# Proving $\int_0^\infty\frac {1}{(1+(x\sin(5x))^2)}dx$ does not converge [duplicate]

I understand that the following improper integral $$\int_0^\infty\frac {1}{1+(x\sin(5x))^2}dx$$ does not converge, and the intuition behind it, but I would very much like to see proof of that.

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Actually this post, linked from 107427 is even more direct match. –  Sasha Jul 25 '12 at 13:36
thanks - will check these posts out –  JohnnyE. Jul 25 '12 at 13:45