Repeated Integration by Parts

Question

Which of the following is equivalent to the indefinite integral $$\displaystyle\int x^2 \sin(x) \, dx$$?

Accepted Answer

$$\displaystyle (2 - x^2) \cos(x) + 2x \sin(x) + C$$

Answer

$$\displaystyle x^2 \cos(x) - 2x \sin(x) + 2 \cos(x) + C$$

Answer

$$\displaystyle -x^2 \cos(x) + 2x \sin(x) + C$$

Answer

$$\displaystyle (x^2 + 2) \sin(x) - 2x \cos(x) + C$$

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