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

Question

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.

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

Answer 1

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 $$\frac{2}{3}t^\frac{3}{2}+C$$