Integral Value Calculation (Jee Mains)

Basics and Substitution

Hard

Integral Value Calculation

Let I(x) = $\int {\frac{{3dx}}{{(4x + 6)(\sqrt {4{x^2} + 8x + 3} )}}}$ 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 ∈ N, gcd(a,b) = 1, then a + b + c is equal to :

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