# Impossible definite integral! [closed]

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'AurizioOct 1 '15 at 19:07

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – TravisJ, mickep, Did, Thomas, Jack D'Aurizio
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• 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. – mickep Oct 1 '15 at 18:58
• Are you sure that the sine should be in the exponential? – 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.