Chapter 5: Integrals - Section 5.4 - The Fundamental Theorem of Calculus - Exercises 5.4 - Page 287: 36

$\dfrac{\ln^2 2}{2}$

Given:$\int_{1}^{2}\frac{\ln x}{x}dx$ Now,we take $\ln x=t$ Differentiate $wrt. x$ on both sides We get, $1/xdx=dt$ And limits from $ 0$ to $\ln 2 $ $\int_{0}^{\ln 2}tdt$ $[\frac{t^2}{2}]_{0}^{\ln 2}$ Now, apply the limits: $\frac{(\ln 2)^2}{2}-0=\dfrac{\ln^2 2}{2}$