How can I integrate by parts this one?

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SUMMARY

The integral of 1/(sqrt[x] * ln[x]) from 2 to infinity cannot be solved due to the function's divergence as x approaches infinity. The integration by parts attempt using u = ln[x] and dv = 1/sqrt(x) leads to an incorrect conclusion, as the integral does not converge. The discussion highlights the necessity of verifying the problem statement, suggesting a possible typo from the professor regarding the integral's formulation.

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Homework Statement



I have to solve the following integral

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

Homework Equations





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!
 
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I don't think \int \frac{dx}{\sqrt{x}*ln(x)} has an antiderivative.

Do you mean \int \frac{ln(x)}{\sqrt{x}}dx ?
 
glomar said:

Homework Statement



I have to solve the following integral

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

Homework Equations





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!

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.
 
Probably it was an error from the Professor. I'll check that.
Thanks!
 

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