If where and

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

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

where

I(0) = \frac{\sqrt{3}}{4} + 20

and

I\left(\frac{1}{2}\right) = \frac{a\sqrt{2}}{b} + c

, for

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

\gcd(a, b) = 1

a + b + c

is equal to