Let I(x) = ∫ 3dx/(4x+6)√(4x²+8x+3) and I(0) = √3/4 + 20. If I(1/2… | JEE Main 2026 Mathematics PYQ

MCQMediumJEE Main 2026 · 23 January, Shift 2Indefinite Integrals

Let $I(x) = \int \frac{3dx}{(4x+6)\sqrt{4x^2+8x+3}}$ and $I(0) = \frac{\sqrt{3}}{4} + 20$ . If $I\left(\frac{1}{2}\right) = \frac{a\sqrt{2}}{b} + c$ , where $a, b, c \in \mathbb{N}, \gcd(a, b) = 1$ , then $a+b+c$ is equal to

A
$29$
B
$28$
C
$30$
D
$31$

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