JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002The integral ∫0π2(x+3)sinx1+3cos2x dx\int_{0}^{\frac{\pi}{2}} \frac{(x + 3) \sin x}{1 + 3 \cos^2 x} \, dx∫02π1+3cos2x(x+3)sinxdx is equal to:AOption A. π3(π+1)\frac{\pi}{\sqrt{3}} (\pi + 1)3π(π+1)BOption B. π3(π+2)\frac{\pi}{\sqrt{3}} (\pi + 2)3π(π+2)COption C. π33(π+6)\frac{\pi}{3\sqrt{3}} (\pi + 6)33π(π+6)DOption D. π23(π+4)\frac{\pi}{2\sqrt{3}} (\pi + 4)23π(π+4)CheckStep-by-step hintSkip · show solution
