Chapter 4.8, Problem 83E

(a)

To determine

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

(b)

To determine

Check whether the anti–derivative term ${\displaystyle \int x\sin x}dx$ for the function $-x\cos x+C$ is right or wrong.

(c)

To determine

Check whether the anti–derivative term ${\displaystyle \int x\sin x}dx$ for the function $-x\cos x+\sin x+C$ is right or wrong.