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Math Help - integral

  1. #1
    Super Member Random Variable's Avatar
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    integral

     \int_{0}^{\infty} \frac{e^{\cos x} \sin (\sin x)}{x} \ dx = \frac{\pi}{2} (e-1)


    It's tempting to say that  \int_{0}^{\infty} \frac{e^{\cos x} \sin (\sin x)}{x} \ dx =  \text{Im} \int_{0}^{\infty} \frac{e^{e^{ix}}}{x} \ dx .


    But  \int_{0}^{\infty} \frac{e^{e^{ix}}}{x} \ dx diverges.


    EDIT: A principal value approach works.
    Last edited by Random Variable; December 21st 2011 at 01:34 PM.
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