\begin{align}
\int \left ( \frac{x+2}{x} \right )^2 dx &= \int \left (1 + \frac{2}{x} \right )^2 dx \\
&= \int \left ( 1 + \frac{4}{x} + \frac{4}{x^2} \right ) dx \\
&= x + 4 \log |x| – \frac{4}{x} + C
\end{align}
積分をしてみる
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\begin{align}
\int \left ( \frac{x+2}{x} \right )^2 dx &= \int \left (1 + \frac{2}{x} \right )^2 dx \\
&= \int \left ( 1 + \frac{4}{x} + \frac{4}{x^2} \right ) dx \\
&= x + 4 \log |x| – \frac{4}{x} + C
\end{align}
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