Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 391: 108

$$\int_{1}^{e^ x} \frac{1}{t} d t=x $$

Given $$\int_{1}^{e^ x} \frac{1}{t} d t $$ So, we have \begin{aligned} I&=\int_{1}^{e^ x} \frac{1}{t} d t\\ &=[\ln |t|]_{1}^{e^ x}\\ &=\ln |e^ x|-\ln 1\\ &=\ln (e^ x)\\ &=x\\ \end{aligned}