what I would do is set up the integral in whatever software you plan to do it in and run it using an increasing upper limit of integration. If the integral has any hope of converging you should start to see evidence of that the results of each run start to get closer and closer. Just keep expanding in upper limit until the
absolute value of the difference between runs is less than some number you're happy with. A little experience will quickly tell you how far you have to integrate to.
It's a sum of decaying exponentials so it should converge, possible very quickly depending on [tex]\lambda[/tex]
If you don't see evidence of convergence well then you have to take a much closer look at things. Cross that bridge when you come to it.
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