Indefinite Integration · Integration by substitution

Let

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

and

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

. If

I\left(\dfrac12\right) = \dfrac{a\sqrt2}{b} + c

, where

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

\gcd(a, b) = 1

, then

a + b + c

is equal to:

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