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Math Help - convergence of an integral

  1. #1
    Super Member Random Variable's Avatar
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    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$ .
    Last edited by Random Variable; August 7th 2011 at 12:43 PM.
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  2. #2
    Super Member Bacterius's Avatar
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    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.
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