$\displaystyle \int \ {x}{arctan(x)}$ is the u $\displaystyle u={x}{arctan(x)}$
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$\displaystyle \int x \arctan{x} \, dx $ $\displaystyle u = \arctan{x}$ ... $\displaystyle dv = x \, dx$ $\displaystyle du = \frac{1}{1+x^2} \, dx$ ... $\displaystyle v = \frac{x^2}{2}$
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