Integral x^2 arctan x dx
+ C\\ &= \frac{1}{3}x^3\arctan x - \frac{1}{6}x^2 + \frac{1}{6}\ln|1+x^2|+C\\ &= \frac{1}{3}x^3\arctan x - \frac{1}{6}x^2 + \frac{1}{6}\ln(1+x^2)+C. \end{align*}$$ If after integration by parts/substitution, the resulting integral is harder than the one you started with, then it's time to go back and try a different integration by ................
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