Chapter 8.2, Problem 49E

a. One way to integrate ${\displaystyle \int x\sqrt{x+1}}dx$ is to use integration by parts. Do so to find the antiderivative.

b. Another way to evaluate the integral in part a is by using the substitution $u=x+1$. Do so to find the antiderivative.

c. Compare the result from the two methods. If they do not look the same, explain how this can happen. Discuss the advantages ad disadvantages of each method.