Ok people, i am very newbie in integration s.
I solved this one, but i dont know if i solved it correctly.
Can u give a look plz.
It's correct! But I would just write:
$\displaystyle \int \frac{\sqrt{1+3\ln(x)}}{x}dx$
Let $\displaystyle \1+3\ln(x)=t \Rightarrow \frac{3dx}{x}=dt \Rightarrow \frac{dx}{x}=\frac{dt}{3}$
So the integral becomes:
$\displaystyle \frac{1}{3}\int \sqrt{t}dt= \frac{2(1+3\ln(x))^{\frac{3}{2}}}{9}+C$
(Don't forget the integration constant)