I'm up against this Laplace transform integral:(adsbygoogle = window.adsbygoogle || []).push({});

$$F(s) ~:=~ \int^\infty_0 \exp\left( -sx + \frac{i\omega}{1+\lambda x} \right) \, dx $$where ##s## is complex, ##\omega## is a real constant, and ##\lambda## is a positive real constant.

By inspection, I think it should converge, at least for some (nontrivial) domain of values for ##s## and ##\omega## (tell me if I'm wrong). But every symbolic integrator I've tried barfs on it.

I figured I should at least ask here before I give up.

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# I Another Integral Challenge

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