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What is the correct answer of this integral?

Posted 11 years ago

hi I have an integral in this form::: NIntegrate[ (5184(-11 + k(98 + k(-16 + k(-40 + k(17 + 2k(7 + k)))))))/ ((1 + E^((1/2)(-1 + k)))(1 + k)^3(-7 + k*(2 + k))^3), {k, 0, Infinity}] when i set , MaxRecursion to 12 answer is of the order of 10^11 when set to 30 answer is of order 10^25 when set 40 order is 10^28 when set to 100 and above order is 10^34 and is constant up to 400 but i have an error in answer. what is the correct answer of this integral? many thanks.

POSTED BY: esi fn

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Posted 11 years ago

It definitely does not converge. There is a nonintegrable singularity at -1 + 2 Sqrt[2]. It is a pole of order 3, hence not integrable. The fact that increasing `MaxRecursion` gives ever more large results is an indication of such a singularity. And `NIntegrate` does issue a warning message to the effect that there might be such a problem.

POSTED BY: Daniel Lichtblau

Posted 11 years ago

After cleaning out the cache, I re calculated, and see a pole at `{{k -> 1.82843},`, which means the integral won't converge. Sorry about the earlier (hasty, poor) post.