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Antiderivative problem

  1. Jul 8, 2010 #1
    1. The problem statement, all variables and given/known data
    I'm working on an infinite series problem and need to find the antiderivative of 1/((x(lnx)^3).

    2. Relevant equations

    3. 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!
  2. jcsd
  3. Jul 8, 2010 #2
    After the u-substitution, what is the integrand in terms of u now?
  4. Jul 8, 2010 #3
    It would be 1/(x(u)^3)
  5. Jul 8, 2010 #4


    Staff: Mentor

    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?
  6. Jul 8, 2010 #5
    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.
  7. Jul 8, 2010 #6


    Staff: Mentor

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

    du/u^3 = u^(-3)du
  8. Jul 8, 2010 #7
    The light finally came on, Thanks!!!
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