Chapter 6.1, Problem 50E

Which of the following is ${\displaystyle \int x\sqrt{x+1}}dx$?

$a.\frac{2}{5}{\left(x+1\right)}^{\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}-\frac{2}{3}{\left(x+1\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}+C$

$b.\frac{1}{2}{x}^2.\frac{2}{3}{\left(x+1\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}+C$