Integration by Parts with Arctan

Question

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

Accepted Answer

$$\displaystyle\frac{x^2 + 1}{2} \arctan(x) - \frac{x}{2} + C$$

Answer

$$\displaystyle\frac{x^2}{2} \arctan(x) - \frac{x}{2} + C$$

Answer

$$\displaystyle\frac{x^2}{2} \arctan(x) + \frac{1}{2} \ln(1 + x^2) + C$$

Answer

$$\displaystyle\frac{x^2 - 1}{2} \arctan(x) + \frac{x}{2} + C$$

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