JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002If ∫ex(xsin−1x1−x2+xln−1x(1−x2)3/2+x1−x2)dx=g(x)+C\int e^x \left( \frac{x \sin^{-1} x}{\sqrt{1-x^2}} + \frac{x \ln^{-1} x}{(1-x^2)^{3/2}} + \frac{x}{1-x^2} \right) dx = g(x) + C∫ex(1−x2xsin−1x+(1−x2)3/2xln−1x+1−x2x)dx=g(x)+C, where CCC is the constant of integration, then g(12)g\left(\frac{1}{2}\right)g(21) equals:AOption A. π4π3\frac{\pi}{4} \sqrt{\frac{\pi}{3}}4π3πBOption B. π6π3\frac{\pi}{6} \sqrt{\frac{\pi}{3}}6π3πCOption C. π43\frac{\pi}{4} \sqrt{3}4π3DOption D. π63\frac{\pi}{6} \sqrt{3}6π3CheckStep-by-step hintSkip · show solution
