MathematicsMedium64×since 2004Q4020For x² ≠\ne= nπ\piπ + 1, n ∈\in∈ N (the set of natural numbers), the integral ∫x2sin(x2−1)−sin2(x2−1)2sin(x2−1)+sin2(x2−1)dx\int {x\sqrt {{{2\sin ({x^2} - 1) - \sin 2({x^2} - 1)} \over {2\sin ({x^2} - 1) + \sin 2({x^2} - 1)}}} dx}∫x2sin(x2−1)+sin2(x2−1)2sin(x2−1)−sin2(x2−1)dx is equal to : (where c is a constant of integration)Aloge∣12sec2(x2−1)∣+c{\log _e}\left| {{1 \over 2}{{\sec }^2}\left( {{x^2} - 1} \right)} \right| + cloge21sec2(x2−1)+cB12loge∣sec(x2−1)∣+c{1 \over 2}{\log _e}\left| {\sec \left( {{x^2} - 1} \right)} \right| + c21logesec(x2−1)+cC12loge∣sec2(x2−12)∣+c{1 \over 2}{\log _e}\left| {{{\sec }^2}\left( {{{{x^2} - 1} \over 2}} \right)} \right| + c21logesec2(2x2−1)+cDloge∣sec(x2−12)∣+c{\log _e}\left| {\sec \left( {{{{x^2} - 1} \over 2}} \right)} \right| + clogesec(2x2−1)+cCheck answerSkip