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# Improper integral of lnx/(e^x) watch

1. Hello everyone,

I need to test the integral of lnx/(e^x) between 1 and infinity for convergence.

I tried to integrate this function, but I can't do it (either by parts or by substitution). So I suppose that I need to use the comparison test. So I checked the answer (and apparently the integral converges), so I am trying to find a function which is greater than lnx/(e^x) between 1 and infinity, and that has an integral which also converges.

I tried (lnx)/x, but it diverges.

Could you help me find a function greater than lnx/(e^x), that has an integral which converges between 1 and infinity?

Thanks
2. Have you tried lnx over higher powers of x?
3. Why not use ?
4. (Original post by Kolya)
Why not use ?
Oh! that totally makes sense!

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