Help solve this integral (by parts possibly)

1. Aug 6, 2015

Engineerbrah

QUESTION:

The question is to find the improper integral of (x^1/2)/lnx dx.

MY ATTEMPT:
1)I tried it byparts, by taking 1/ln x as 'u' or the first function but i got stuck.

2)Alternatively, I tried substituting x=e^2t in hopes to eliminate ln for a simpler byparts integration, but that didn't work
out.

2. Aug 6, 2015

Devin

You can apply parts directly. Apply parts in the form such that the evaluation of the new integral involves the derivative of (1/lnx).

3. Aug 6, 2015

Engineerbrah

I tried it this way. The furthest I got was

(2*(x)^(1/2))/lnx - Integral of (2/((x)^(1/2))(lnx)^2 dx

Still not able to attain the answer.

4. Aug 6, 2015

Devin

I believe this to be the way to approach. Then the evaluation of the new integral is straightforward.

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Last edited by a moderator: Aug 6, 2015