Question

$\int \frac{1}{x}{\left(\log x\right)}^{2}dx$

Answer 1

$$\begin{gathered} \int \frac{1}{x}{\left(\log x\right)}^{2}dx \\ \mathrm{Let}\log x=t \\ \Rightarrow \frac{1}{x}dx=dt \\ \mathrm{Now},\int \frac{1}{x}{\left(\log x\right)}^{2}dx \\ =\int t^{2}dt \\ =\frac{t^3}{3}+\mathrm{C} \\ =\frac{{\left(\log x\right)}^3}{3}+\mathrm{C} \end{gathered}$$