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Improper intergral

Posted 9 years ago

Hi, I'm trying to compute the following improper integral: exp(-x)/Log(x) at the [2,+inf) interval and it returns me that it's not converges. But this integral should converge, as I see it by comparison test with exp(-x). Can somebody explain me what's wrong here?

Code: Integrate[1/(E^x*Log[x]), {x, 2, [Infinity]}] thanks

POSTED BY: Sasha ros
3 Replies
Posted 9 years ago

I got it, thanks for your help

POSTED BY: Sasha ros

Yes. By comparison to Integrate[1/(E^x), {x, 2, Infinity}], it should converge.

I think this is just an error in the system which triggers that message. Thank you for letting us know about this issue. I've forwarded it to the developers so they can take a look into the issue.

Integrate doesn't seem to find a symbolic solution to the problem. One might still exist... probably with some obscure function... or with some very difficult derivation, but Integrate doesn't find it if it does exist. You can however use NIntegrate as shown above to get a numeric value.

POSTED BY: Sean Clarke
Posted 9 years ago

Use NIntegrate;

In[56]:= NIntegrate[1/(E^x*Log[x]), {x, 2, \[Infinity]}]

Out[56]= 0.136743

This integral is indeed converging as can be seen from:

Plot[NIntegrate[1/(E^x*Log[x]), {x, 2, upper}], {upper, 2, 10}]

enter image description here

POSTED BY: Erik Mahieu
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