JEE Main 202127 Aug, Evening shiftMathematicsMediumIntegral Calculus369× since 2002The value of the integral ∫01xdx(1+x)(1+3x)(3+x)\int\limits_0^1 {{{\sqrt x dx} \over {(1 + x)(1 + 3x)(3 + x)}}}0∫1(1+x)(1+3x)(3+x)xdx is :AOption A. π8(1−32){\pi \over 8}\left( {1 - {{\sqrt 3 } \over 2}} \right)8π(1−23)BOption B. π4(1−36){\pi \over 4}\left( {1 - {{\sqrt 3 } \over 6}} \right)4π(1−63)COption C. π8(1−36){\pi \over 8}\left( {1 - {{\sqrt 3 } \over 6}} \right)8π(1−63)DOption D. π4(1−32){\pi \over 4}\left( {1 - {{\sqrt 3 } \over 2}} \right)4π(1−23)CheckSkip · show solution
