Chapter 4.8, Problem 85E

(a)

To determine

Check whether the anti–derivative term ${{\displaystyle \int \left(2x+1\right)}}^{2}dx$ for the function $\frac{{\left(2x+1\right)}^3}{3}+C$ is right or wrong.

(b)

To determine

Check whether the anti–derivative term ${{\displaystyle \int 3\left(2x+1\right)}}^{2}dx$ for the function ${\left(2x+1\right)}^3+C$ is right or wrong.

(c)

To determine

Check whether the anti–derivative term ${{\displaystyle \int 6\left(2x+1\right)}}^{2}dx$ for the function ${\left(2x+1\right)}^3+C$ is right or wrong.