Improper Integrals with u sub and integration by parts ?

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Homework Help Overview

The discussion revolves around evaluating the improper integral from 1 to infinity of (lnx)/(x) dx, focusing on techniques such as u-substitution and integration by parts.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the choice of "u" for u-substitution and the necessity of integration by parts. There is also a focus on determining the convergence or divergence of the integral and the steps needed to evaluate it.

Discussion Status

Some participants have provided guidance on using u-substitution, while others are exploring the implications of convergence and the evaluation process. Multiple interpretations of the problem are being discussed, particularly regarding the methods to apply.

Contextual Notes

There is an emphasis on the need to evaluate the integral as an improper integral, and participants are considering the limits involved in this evaluation.

Jay J
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Homework Statement



The integral from 1 to infinity of (lnx)/(x) dx

Homework Equations


U substitution and integration by parts


The Attempt at a Solution


Cant decide what to use as my "u" . . can anyone help with this part ?

-Jay J-
 
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this doesn't really require integration by parts, just a u-substitution:

[tex]\int \frac{ln(x)}{x}=\int u du = \frac{1}{2}u+ C= \frac{1}{2}(ln(x))^2+C[/tex]

here you take u = ln(x) and differentiate to get, du = 1/x dx.
 
ok i understand the whole u substitution part but then i have to determine whether or not the integral is divergent or convergent and if its convergent i have 2 evaluate it . .. how would you do that ?

-Jay J-
 
Evaluate the integral between x=0 and x=M and let M approach infinity. What do you conclude?
 

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