How Do You Integrate (x^(1/2))/ln(x) Using Integration by Parts?

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Homework Help Overview

The discussion revolves around finding the improper integral of (x^(1/2))/ln(x) using integration by parts. Participants are exploring various methods to tackle this integral, which involves logarithmic and algebraic functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants describe attempts using integration by parts, with one suggesting taking 1/ln(x) as 'u'. Others mention trying substitutions like x=e^(2t) to simplify the integration process. There are also discussions about the challenges faced in evaluating the resulting integrals.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and the difficulties encountered. Some guidance has been offered regarding the application of integration by parts, but there is no consensus on a definitive approach or solution yet.

Contextual Notes

Participants are working under the constraints of improper integrals and the complexities introduced by the logarithmic function. There is a focus on finding a suitable method without providing complete solutions.

Engineerbrah
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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.

Please help asap. Thanks.
 
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Engineerbrah said:
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.

Please help asap. Thanks.
You can apply parts directly. Apply parts in the form such that the evaluation of the new integral involves the derivative of (1/lnx).
 
Devin said:
You can apply parts directly. Apply parts in the form such that the evaluation of the new integral involves the derivative of (1/lnx).

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.
 
Engineerbrah said:
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.
Devin said:
You can apply parts directly. Apply parts in the form such that the evaluation of the new integral involves the derivative of (1/lnx).
I believe this to be the way to approach. Then the evaluation of the new integral is straightforward.

<Mod note: attachment deleted>
 
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