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Full solution for integral (lnx ^ 1/2) / x dx

GROUPS:

Good night!

In resolving the integral (lnx ^ 1/2) / x dx could not understand where it came 4th in the denominator.

Thank you!

Answer
11 months ago

Hi,

the way you write your problem is not quite clear, because it does not state clearly where the parenthesis are meant to be.

Do you mean:

Integrate[ (Log[x^(1/2)])/x, x]

which gives $\frac{\log^2 (x)}{4}$, or do you mean

Integrate[ (Log[x]^(1/2))/x, x]

which gives $\frac{2}{3} \log^\frac{3}{2} (x)$, or do you mean something else? It would be helpful if you pasted the Mathematica function into your question.

For the step-by-step solutions, see below.

Cheers,

Marco

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POSTED BY: Marco Thiel
Answer
11 months ago

Got it! Thank you very much!

POSTED BY: Updating Name
Answer
11 months ago