Question

Evaluate: $\int \frac{\log x}{x}dx$

Answer 1

$$\begin{gathered} \mathrm{Let}I=\int \frac{\log x}{x}dx \\ \&\mathrm{let}\log x=t \\ \Rightarrow \frac{1}{x}dx=dt \\ \therefore I=\int t·dt \\ =\frac{t^2}{2}+C \\ =\frac{{\left(\log x\right)}^2}{2}+C\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\left(\mathit{\because }t=\log \mathit{}x\right) \end{gathered}$$