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\newcommand\ds{\displaystyle}
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QUESTION

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

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ANSWER

$\ds\int\left(1+\frac{1}{x}\right)^2\,dx
=\int\left(1+\frac{2}{x}+\frac{1}{x^2}\right)\,dx
=\int1\,dx+\int\frac{2}{x}\,dx+\int x^{-2}\,dx
=x+2\ln|x|-\frac{1}{x}+c$




\end{document}
