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Indefinite Integration with Logarithms and Substitution

  1. Dec 6, 2009 #1
    Hi, I missed a few days of my calculus class. I've managed to figure out how to use substitution to solve an indefinite integral, and can apply the log properties to some extent. I just can't figure out this problem.

    1. The problem statement, all variables and given/known data
    Find the indefinite integral:
    [tex]\int{\frac{1}{x ln(x^3)}}dx[/tex]

    2. The attempt at a solution
    Well, since d/dx ln(x) is u'/u I know something is kinda wack with the bottom. I first tried to substitute with u=x^3, but then du is 3x^2 and there is only x on the bottom not x squared. I then thought it might be backwards, since the x on bottom is like x^-1 and it would have an integral with a natural log in it, but that wasn't really working out either.

    I'm pretty stumped, I've attempted it several times.

    Thanks for your help!
     
  2. jcsd
  3. Dec 6, 2009 #2
    Hint: ln(x^3)=3ln(x).
     
  4. Dec 6, 2009 #3
    I hate it when that happens. so 1/3*ln|ln(x)|

    Thanks grief!
     
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