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\newcommand\ds{\displaystyle}
\begin{document}

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QUESTION

Find $\ds\int\frac{x^2}{x^2+1}\,dx$.

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ANSWER

$\ds\int\frac{x^2}{x^2+1}\,dx= \int\frac{(x^2+1)-1}{x^2+1}\,dx=
\int\left(1-\frac{1}{x^2+1}\right)\,dx=x-\tan^{-1}x+c$




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