# Math Help - convergence of an integral

1. ## convergence of an integral

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

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

2. ## Re: convergence of an integral

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.