What is the correct answer of this integral?

Questions
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1

hi
I have an integral in this form:::

 NIntegrate[
   (5184*(-11 + k*(98 + k*(-16 + k*(-40 + k*(17 + 2*k*(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.

2

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.

3

If I change NIntegrate to Integrate, I get a msg that the Integral does not converge.

4

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.