Chapter 5.10, Problem 23ES

(a) Use Formula $\left(18\right)$ to find

$\frac{d}{dx}{\displaystyle {\int }_1^{x^2}t\sqrt{1+t}dt}$

(b) Use a CAS to evaluate the integral and differentiate the resulting function.

(c) Use the simplification command of the CAS, if necessary, to confirm that the answers in parts (a) and (b) are the same.