Chapter 5.10, Problem 15ES

Find the derivative using Formula $\left(18\right)$ , and check your answer by evaluating the integral and then differentiating the result.

(a) $\frac{d}{dx}{\displaystyle {\int }_1^{x^3}\frac{1}{t}dt}$

(b) $\frac{d}{dx}{\displaystyle {\int }_1^{\ln x}{e}^{t}dt}$