Question

Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]

Answer 1

\[\text{ Let I } = \int\frac{\log x}{x} dx\]
\[\text{ and }\text{  let} \log x = t\]
\[ \Rightarrow \frac{1}{x} dx = dt\]
\[ \therefore I = \int t \cdot dt\]
\[ = \frac{t^2}{2} + C\]
\[ = \frac{\left( \log x \right)^2}{2} + C \left( \because t = \log x \right)\]