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Homework Help: How can I integrate by parts this one?

  1. May 17, 2009 #1
    1. The problem statement, all variables and given/known data

    I have to solve the following integral

    1/(sqrt[x] * ln[x]) from 2 to infinity

    2. Relevant equations

    3. The attempt at a solution

    u= ln[x] dv=1/sqrt(x)
    du= 1/x v= 2 sqrt(x)

    If I do this I get

    lim (ln b/ sqrt[x] - 4 sqrt[x] - ln2/sqrt[x] + 4 sqrt[x])

    Is this the actual result of the integral? Did I substitute correctly?
    Thanks in advance!
  2. jcsd
  3. May 17, 2009 #2
    I don't think [tex] \int \frac{dx}{\sqrt{x}*ln(x)} [/tex] has an antiderivative.

    Do you mean [tex] \int \frac{ln(x)}{\sqrt{x}}dx [/tex] ?
  4. May 18, 2009 #3
    This problem can not be solved because the function is not strictly converging towards infinity. You can calculate definite integrals, f.ex. [2,100 000], [2, 1 000 000] and so on, but there is no way this integral reaches a certain limit as x goes towards infinity. I agree with Random Variable, this seems lik a typo.
  5. May 18, 2009 #4
    Probably it was an error from the Professor. I'll check that.
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