Let I(x)=∫(3 dx)/((4x+6)(√(4x²+8x+3))) and I(0)=(3)/4+20. If I(1/2)=(a 2)/b+c, where a, b, c, gcd (a, b)=1, then a+b+c is equal to

Integral Calculus: JEE Main 2026 Mathematics question

JEE Main 2026 · 23 Jan, Evening shift · Q8

JEE Main 202623 Jan, Evening shiftMathematicsEasyIntegral Calculus369× since 2002

Let

I(x)=\int\frac{3\,dx}{(4x+6)\left(\sqrt{4x^2+8x+3}\right)}

and

I(0)=\frac{\sqrt3}{4}+20

. If

I\left(\frac12\right)=\frac{a\sqrt2}{b}+c

, where

a, b, c\in\mathbb{N}

\gcd(a, b)=1

, then

a+b+c

is equal to

JEE Main 2026 · 23 Jan, Evening shift · Q8

JEE Main 202623 Jan, Evening shiftMathematicsEasyIntegral Calculus369× since 2002

Let

I(x)=\int\frac{3\,dx}{(4x+6)\left(\sqrt{4x^2+8x+3}\right)}

and

I(0)=\frac{\sqrt3}{4}+20

. If

I\left(\frac12\right)=\frac{a\sqrt2}{b}+c

, where

a, b, c\in\mathbb{N}

\gcd(a, b)=1

, then

a+b+c

is equal to