教科書基本レベル
$$\begin{align*}\int\dfrac{1}{x^{2}-1}dx & =\dfrac{1}{2}\int\left(\dfrac{1}{x-1}-\dfrac{1}{x+1}\right)dx\\& =\dfrac{1}{2}\left(\log\left|x-1\right|-\log\left|x+1\right|\right)+C\\& =\dfrac{1}{2}\log\left|\dfrac{x-1}{x+1}\right|+C\end{align*}$$
