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Improper Integrals with u sub and integration by parts ?

  • Thread starter Jay J
  • Start date
  • #1
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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 any one help with this part ?

-Jay J-
 

Answers and Replies

  • #2
kreil
Insights Author
Gold Member
668
67
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.
 
  • #3
26
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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-
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Evaluate the integral between x=0 and x=M and let M approach infinity. What do you conclude?
 

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