정적분 $\displaystyle \int _ {1} ^ {2} {\frac{1} {x ^ {2}} \sqrt {\frac{x-1} {x+1}} dx}$ 를 구하시오.

• ①$\displaystyle \frac{\pi} {3} - \frac{\sqrt {3}} {2}$
• ②$\displaystyle \frac{\pi} {3} - \frac{1} {2}$
• ③$\displaystyle \frac{\pi} {3} + \frac{1} {2}$
• ④$\displaystyle \frac{\pi} {3} + \frac{\sqrt {3}} {2}$