Is it possible to calculate this integral?

$$ \int_{0}^{+\infty}\exp\left(-a\sqrt{b^2+x^2}\right)\sin(cx)\frac{dx}{x}$$

I'm tired of it. I almost used any method to calculate this definite integral. It seems there is no analytic solution. I need help. Thank you.


closed as off-topic by TravisJ, mickep, Did, Thomas, Jack D'Aurizio Oct 1 '15 at 19:07

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  • 1
    $\begingroup$ Hi and welcome to Math.SE. While being tired of it, could you please update your question using mathjax? Also, please improve the title. Finally, please show some effort/discuss what is the problem/difficulty, or at least give some context. $\endgroup$ – mickep Oct 1 '15 at 18:58
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    $\begingroup$ Are you sure that the sine should be in the exponential? $\endgroup$ – Ron Gordon Oct 1 '15 at 19:13

It is not converging. If $c\neq 0$, we have divergence on a neighbourhood of $\frac{3\pi}{2|c|}+\frac{2\pi}{|c|}\mathbb{Z}$.

If $c=0$, we have a non-integrable singularity in the origin.

  • $\begingroup$ Before it was mathjax'd I read it as if the sine was outside the exponential function (now I checked, and it was not). After all, the title of the question was not bad... $\endgroup$ – mickep Oct 1 '15 at 19:12

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