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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
5 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
5 months ago

Got it! Thank you very much!

POSTED BY: Updating Name
Answer
5 months ago