Answer
$$\int\frac{(\ln x)^2}{x}dx=\frac{(\ln x)^3}{3}+C$$
Work Step by Step
$$A=\int\frac{(\ln x)^2}{x}dx$$
Let $u=\ln x$.
Then $du=\frac{1}{x}dx$
Substitute into $A$, we have $$A=\int u^2du$$ $$A=\frac{u^3}{3}+C$$ $$A=\frac{(\ln x)^3}{3}+C$$