# $\int\frac{\sqrt{\ln x}}{x}\ dx$

I've been trying to figure this one out for a while now, but I seem to get stuck.. I would guess integration by parts is the preferred method to use? But I end up with either an error function or an answer the same as the original function.

$\int\frac{\sqrt{\ln x}}{x}\ dx$

• Did you try substituting $u=\ln x$? It becomes $\int\sqrt{u}\ du$. – Gregory Grant Dec 26 '15 at 19:54

setting $t=\ln(x)$ then we get $$dt=\frac{1}{x}dx$$ then we get $$\int \sqrt{t}dt$$ the last integral is given by $$\frac{2}{3}t^\frac{3}{2}+C$$
• Then the answer would be $1/ 2 \sqrt ln(t)$? computer gives me 2/3 Log[x]^(3/2) as correct answer – Alex L Dec 26 '15 at 20:18
• i used the following rule $\int x^ndx=\frac{x^{n+1}}{n+1}$ for $n\ne -1$ – Dr. Sonnhard Graubner Dec 26 '15 at 20:27