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
