Improper Integrals - Infinite Intervals

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SUMMARY

The discussion centers on evaluating the improper integral from e to infinity of the function 25/(x(lnx)^3) dx. The user initially attempted integration by parts but found it unproductive. The correct approach involves using the substitution u = ln(x), which simplifies the evaluation process and leads to a successful resolution of the integral. This method is confirmed as effective by another forum participant.

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forestmine
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Improper Integrals -- Infinite Intervals

Homework Statement



Evaluate the integral.

(from e to infinity) ∫(25/x(lnx)^3)dx

Homework Equations




The Attempt at a Solution



I know that for evaluating improper integrals, you can take the limit as t approaches infinity of the given integral, but my problem is in evaluating the integral itself.

25 comes out of the integrand, and so I'm left with dx/x(lnx)^3, and this is where I'm confused. I'm guessing integration by parts is necessary to properly evaluate this, but I'm not entirely sure. I tried setting u = (lnx)^-3, which gives me du=-3lnx/x*dx, but then I'm left with dv=xdx, so v=1/2x^2, but based on the solution, I don't believe I'm at all headed in the right direction.

Any help would be greatly appreciated!
 
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forestmine said:
I'm guessing integration by parts is necessary to properly evaluate this,


Use the substitution u=ln(x) instead.


ehild
 


I did exactly that and it works out perfectly.

Thanks a lot!
 

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