Integrate the rational functions $\frac{1}{x^4-1}$

Question

$\begin{array}{1 1} \frac{1}{4} \log \big | \frac {x-1}{x+1} \big | -\frac{1}{2}\tan^{-1}x+c \\ \frac{1}{4} \log \big | \frac {x+1}{x-1} \big | -\frac{1}{4}\tan^{-1}x+c \\\frac{1}{4} \log \big | \frac {x^2}{x-1} \big | -\frac{1}{2}\tan^{-1}x+c \\ \frac{1}{4} \log \big | \frac {x^2}{x+1} \big | +\frac{1}{2}\tan^{-1}x+c\end{array} $