Antiderivative problem

  • Thread starter stau40
  • Start date
  • #1
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Homework Statement


I'm working on an infinite series problem and need to find the antiderivative of 1/((x(lnx)^3).


Homework Equations


u=lnx


The Attempt at a Solution


I know I have to use the substitution u=lnx, but I still can't figure out what the answer is. I know the antiderivative of 1/((x(lnx)) is ln(lnx) but the third power in my problem is giving me trouble. Any advice? Thanks!
 

Answers and Replies

  • #2
867
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After the u-substitution, what is the integrand in terms of u now?
 
  • #3
37
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It would be 1/(x(u)^3)
 
  • #4
35,134
6,882
It would be 1/(x(u)^3)
When you make a substitution, replace everything. Here you still have a factor of x remaining. If u = ln(x), what is x in terms of u? Also, and this is related, did you replace dx by its appropriate expression involving du?
 
  • #5
37
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Ok, it should be the antiderivative of du/(u^3) but I still don't understand how to work thru the third power. If I solve for the antiderivative and end up with u^4 I would need (1/4) in front of u and that gets me to the wrong result.
 
  • #6
35,134
6,882
Ok, it should be the antiderivative of du/(u^3) but I still don't understand how to work thru the third power. If I solve for the antiderivative and end up with u^4 I would need (1/4) in front of u and that gets me to the wrong result.

Well, yes. You can't go from du/u^3 to u^4.

du/u^3 = u^(-3)du
 
  • #7
37
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The light finally came on, Thanks!!!
 

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