- #1

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[tex]\int_0^{\infty}\frac{1}{x^2}\exp\left(\frac{A}{x}-x\right)E_1\left(B+\frac{A}{x}\right)\,dx[/tex]

where ##E_1(.)## is the exponential integral function, and ##A## and ##B## are non-zero positive constants. I tried to find this integral in the table of integrals, but couldn't find it. Next best thing to do is to evaluate this integral numerically, I guess. So, I resorted to Mathematica for that purpose, and used the Nintegrate command, but I got a message that

*the integrand has evaluated to overflow, indeterminate, or infinity.*It suggested to increase the number of recursive refinements, but it didn't work. Is there something fundamentally wrong in the integral, or it's just a technical issue, and how to overcome it? I have to mention that when I replaced the lower bound of the integral by a very small value that is greater than 0, the integral was calculated perfectly. Is this the problem maybe?

Thanks