convergence of an integral

**Random Variable** · August 7th 2011, 11:32 AM

Does $\int_{0}^{\infty} \frac{\sin(\tan x)}{x} \ dx$ converge?

A plot of the integrand shows that it oscillates wildly near $x= \frac{\pi}{2} + \pi n$$ .

**Bacterius** · August 7th 2011, 01:51 PM

Would integrating by parts allow the integral of the periodic function $\sin{\tan{x}}$ to be rewritten as a sum? Then you could prove the sum diverges and therefore the integral diverges too. Haven't tried but it seems it would work.

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