$\displaystyle \int _ {- \infty} ^ {\infty} {\frac{1} {\left (1+x^2 \right) ^6}} dx$ 의 Cauchy 주치(Cauchy principal value)를 계산하면?

• ①$\displaystyle \frac{9! \pi} {2^ {11} \left (5! \right) ^2}$
• ②$\displaystyle \frac{9! \pi} {2^ {10} \left (5! \right) ^2}$
• ③$\displaystyle \frac{10! \pi} {2^ {10} \left (5! \right) ^2}$
• ④$\displaystyle \frac{10! \pi} {2^9 \left (5! \right) ^2}$