The value of the integral \(\int_{-1 / 2}^{1 / 2}\left\{\left(\frac{x+1}{x-1}\right)^{2}+\left(\frac{x-1}{x+1}\right)^{2}-2\right\}^{1 / 2} d x\) is equal to
(A) \(\log _{e}\left(\frac{4}{3}\right)\)
(B) \(4 \log _{\mathrm{e}}\left(\frac{3}{4}\right)\)
(C) \(4 \log _{\mathrm{e}}\left(\frac{4}{3}\right)\)
(D) \(\log _{e}\left(\frac{3}{4}\right)\)