Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 390: 23

$$\frac{1}{x} \sin x $$

Given $$ y=\int_{0}^{\ln x} \sin e^{t} d t $$ by using the fundamental theorem, we get \begin{align*} \frac{dy}{dx} &= \sin (e^{\ln x}) \frac{d}{dx} \left( \ln x\right)\\ &=\frac{1}{x} \sin x \end{align*}