Evaluate $\int_1^2 \frac{\log x}{x}\,dx$.

Explanation

1. 01

   Put $t = \log x$, $dt = \frac{dx}{x}$; the limits become 0 and $\log 2$.

2. 02

   $\int_0^{\log 2} t\,dt = \frac{(\log 2)^2}{2}$.