Find the antiderivative/primitive/integrals of the \( \mathrm{P} \)...

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Find the antiderivative/primitive/integrals of the
\( \mathrm{P} \) following by simple manipulation/simplifying.

W
\[
\int \frac{1+2 x^{2}}{x^{2}\left(1+x^{2}\right)} d x
\]
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