Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 335: 63

$F^{\prime}(x)=\displaystyle \frac{1}{x}$

Use the Second Fundamental Theorem of Calculus (Th 4.11) $\displaystyle \frac{d}{dx}\left[\int_{a}^{x}f(t)dt\right] =f(x)$ here: a=1, and f(t)$=\displaystyle \frac{1}{t}$ $F^{\prime}(x)=f(x)=\displaystyle \frac{1}{x}$