${x^2} \ne n\pi + 1, n \in N$ (प्राकृत संख्याओं का समुच्चय) के लिए,समाकलन $\int {x\sqrt {\frac{{2\sin \left( {{x^2} - 1} \right) - \sin 2\left( {{x^2} - 1} \right)}}{{2\sin \left( {{x^2} - 1} \right) + \sin 2\left( {{x^2} - 1} \right)}}} } dx$ क्या है?

• A
  ${\log _e}\left| {\frac{1}{2}{{\sec }^2}\left( {{x^2} - 1} \right)} \right| + c$
• B
  $\frac{1}{2}{\log _e}\left| {\sec \left( {{x^2} - 1} \right)} \right| + c$
• C
  $\frac{1}{2}{\log _e}\left| {{{\sec }^2}\left( {\frac{{{x^2} - 1}}{2}} \right)} \right| + c$
• D
  ${\log _e}\left| {\sec \left( {\frac{{{x^2} - 1}}{2}} \right)} \right| + c$