MathematicsMedium64×since 2004Q4033If ∫1x1−x1+xdx=g(x)+c\int {{1 \over x}\sqrt {{{1 - x} \over {1 + x}}} dx = g(x) + c}∫x11+x1−xdx=g(x)+c, g(1)=0g(1) = 0g(1)=0, then g(12)g\left( {{1 \over 2}} \right)g(21) is equal to :Aloge(3−13+1)+π3{\log _e}\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right) + {\pi \over 3}loge(3+13−1)+3πBloge(3+13−1)+π3{\log _e}\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right) + {\pi \over 3}loge(3−13+1)+3πCloge(3+13−1)−π3{\log _e}\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right) - {\pi \over 3}loge(3−13+1)−3πD12loge(3−13+1)−π6{1 \over 2}{\log _e}\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right) - {\pi \over 6}21loge(3+13−1)−6πCheck answerSkip