JEE Main 202623 Jan, Morning shiftMathematicsEasyIntegral Calculus369× since 2002Let f(x)=∫(2−x2)ex(1+x)(1−x)3/2dxf(x)=\int\frac{(2-x^2)e^x}{(\sqrt{1+x})(1-x)^{3/2}}dxf(x)=∫(1+x)(1−x)3/2(2−x2)exdx. If f(0)=0f(0)=0f(0)=0, then f(12)f\left(\frac{1}{2}\right)f(21) is equal to :AOption A. 2e−1\sqrt{2e}-12e−1BOption B. 2e+1\sqrt{2e}+12e+1COption C. 3e+1\sqrt{3e}+13e+1DOption D. 3e−1\sqrt{3e}-13e−1CheckSkip · show solution
